Pertidaksamaan Matematika: Linear, Kuadrat, Akar, Pecahan, Mutlak – Contoh Soal dan Jawaban

Pertidaksamaan dalam matematika adalah kalimat/pernyataan matematika yang menunjukkan perbandingan ukuran dua objek atau lebih.

Notasi tanda pertidaksamaan matematika

Notasi	Arti	Contoh
<	lebih kecil kurang dari	2 < 3 x + 1 < 3
>	lebih besar lebih dari	3 > 2 3x + 1 > 5
≤	lebih kecil atau sama dengan batas dibawah maksimum maksimal sebanyaknya paling banyak tidak lebih dari sekurangnya	2 ≤ 3 x + 1 ≤ 3
≥	lebih besar atau sama dengan batas diatas minimum minimal sesedikitnya paling sedikit tidak kurang dari selebihnya	3 ≥ 2 3x + 1 ≥ 5
≠	tidak sama dengan	2 ≠ 3 x + 1 ≠ 3
a < x < b	diantara a dan b	2 < x < 5
a ≤ x < b	diantara a dan b bila nilai minimal a	2 ≤ x < 5
a < x ≤ b	diantara a dan b bila maksimal b	2 < x ≤ 5
a ≤ x ≤ b	diantara a dan b bila minimal a dan maksimal b	2 ≤ x ≤ 5

Jenis-jenis pertidaksamaan matematika

1. Pertidaksamaan Linear

Tentukan nilai x dari pertidaksamaan $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f7a24b0e441ab63d2a78b9b926774c25d2e9837" alt="{\displaystyle 6x-7<5x+3}" width="6926.9" height="1008.6">$ !

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f7a24b0e441ab63d2a78b9b926774c25d2e9837" alt="{\displaystyle 6x-7&lt;5x+3}" width="6926.9" height="1008.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/876241ca541cc723a82afcbe7b75ae4b40665ae5" alt="{\displaystyle 6x-5x&lt;3+7}" width="6926.9" height="1008.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbbd105ba9ef2bc5acf7f879c5935b9917585405" alt="{\displaystyle x&lt;10}" width="2907.6" height="936.9"> <img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d8bb9a83fdda391c99c22c792207d72a9937d90c" alt="{\displaystyle HP=\{x|x&lt;10,x\in R\}}" width="10733.8" height="1223.9">

Tentukan nilai x dari pertidaksamaan $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4a2440e367a9ed7a9ce702b4916b6898491d6cb" alt="{\displaystyle 5-2x\geq 4x-1}" width="6926.9" height="1008.6">$ !

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4a2440e367a9ed7a9ce702b4916b6898491d6cb" alt="{\displaystyle 5-2x\geq 4x-1}" width="6926.9" height="1008.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c8f0681897b1b00eeea1554e216d0a5f39f6d0e" alt="{\displaystyle -2x-4x\geq -1-5}" width="8483.9" height="1008.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/26001aa757b8131215cc8653066798431a213a0b" alt="{\displaystyle -6x\geq -6}" width="4464.6" height="1008.6">

(karena nilai negatif maka tanda harus terbalik)

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97bc1f8c61d5129d13278e6ee53069a1736ce3c0" alt="{\displaystyle x\leq 1}" width="2407.1" height="1008.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5085df425b4b4573eed2e3338f0914b8302140f8" alt="{\displaystyle HP=\{x|x\leq 1,x\in R\}}" width="10233.3" height="1223.9">

2. Pertidaksamaan Kuadrat

Tentukan nilai x dari pertidaksamaan $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b5185f96fada10ca921798170a3c20967243539" alt="{\displaystyle x^{2}-7x>10-4x}" width="7953.4" height="1223.9">$ !

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b5185f96fada10ca921798170a3c20967243539" alt="{\displaystyle x^{2}-7x&gt;10-4x}" width="7953.4" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43ba6542d5cd02768c5c3d4cf5d99c52feb46bb5" alt="{\displaystyle x^{2}-3x-10&gt;0}" width="7380.9" height="1223.9">

dibuat dengan harga nol

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63359d5936be87932720637f5d57fd087e402470" alt="{\displaystyle x^{2}-3x-10=0}" width="7380.9" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6de3518a50a15f2f0d46aa9cb6d44ec48bcc4750" alt="{\displaystyle (x+2)(x-5)=0}" width="7984.4" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6d2f9e2ae2758f41ec9d8742f8b751bc7b0a69d" alt="{\displaystyle x=-2\lor x=5}" width="6704.6" height="1008.6">

dibuat irisan

-2	5
+++	N/A	—-	N/A	+++

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebb1909906a62fcec0a9555c1714c868f7b21b24" alt="{\displaystyle HP=\{x|x&lt;-2\lor x&gt;5,x\in R\}}" width="14530.8" height="1223.9">

Tentukan nilai x dari pertidaksamaan $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e33c9ea63b7fb56ddb329d68f16ab395758c5ffd" alt="{\displaystyle 2-x^{2}\leq x-10}" width="6880.4" height="1223.9">$ !

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e33c9ea63b7fb56ddb329d68f16ab395758c5ffd" alt="{\displaystyle 2-x^{2}\leq x-10}" width="6880.4" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f67d8e89833c5329e7913e5488be6ac626728b6f" alt="{\displaystyle x^{2}+x-12\geq 0}" width="6880.4" height="1223.9">

dibuat harga nol

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebe2b120881d716c5962a5e7a349cbd59c3559b9" alt="{\displaystyle x^{2}+x-12=0}" width="6880.4" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/56e1d5997b8769cf7f310f0b42e4c0340ea31c44" alt="{\displaystyle (x+4)(x-3)=0}" width="600" height="400">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8cf43ebe5dc4c1626cd3925fb78edf1ee814d130" alt="{\displaystyle x=-4\lor x=3}" width="6704.6" height="1008.6">

dibuat irisan

(-4)	(3)
+++	N/A	—-	N/A	+++

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1341f03390f17c282a687508d92de48aba365b61" alt="{\displaystyle HP=\{x|x\leq -4\lor x\geq 3,x\in R\}}" width="14530.8" height="1223.9">

3. Pertidaksamaan Akar

Dalam bentuk pertidaksamaan akar sebagai berikut:

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/176c97e80018ffb47352136cf177f8ccde616d1f" alt="{\displaystyle {\sqrt {f(x)}}&lt;0}" width="4737.1" height="2085">

atau

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffbb18d5626b28ad2a2870b9d6039896f29c5621" alt="{\displaystyle {\sqrt {f(x)}}&gt;0}" width="4737.1" height="2085">

haruslah mempunyai syarat yaitu f(x) ≥ 0.

Tentukan nilai x dari pertidaksamaan $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dddac9af6c5a39ebcb74a9d25e69427b32b6a8c2" alt="{\displaystyle {\sqrt {x^{2}-4x}}<{\sqrt {10-x}}}" width="9286.9" height="1510.9">$ !

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dddac9af6c5a39ebcb74a9d25e69427b32b6a8c2" alt="{\displaystyle {\sqrt {x^{2}-4x}}&lt;{\sqrt {10-x}}}" width="9286.9" height="1510.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41c3ba91db366d4bc36eedbc049b6a40dbddf1a8" alt="{\displaystyle ({\sqrt {x^{2}-4x}})^{2}&lt;({\sqrt {10-x}})^{2}}" width="11752.7" height="1510.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/090fd1460bb5e4549ec815c910511278f2740fa0" alt="{\displaystyle x^{2}-4x&lt;10-x}" width="7452.9" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3e46d34c393bc1b9624f1e3abbbd8a13bd8cd69a" alt="{\displaystyle x^{2}-3x-10&lt;0}" width="7380.9" height="1223.9">

dibuat harga nol

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63359d5936be87932720637f5d57fd087e402470" alt="{\displaystyle x^{2}-3x-10=0}" width="7380.9" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6de3518a50a15f2f0d46aa9cb6d44ec48bcc4750" alt="{\displaystyle (x+2)(x-5)=0}" width="7984.4" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6d2f9e2ae2758f41ec9d8742f8b751bc7b0a69d" alt="{\displaystyle x=-2\lor x=5}" width="6704.6" height="1008.6">

dibuat irisan

-2	5
+++	N/A	—-	N/A	+++

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ba67fd59ad724ef087f659f0e0a8d155abff7d8" alt="{\displaystyle -2&lt;x&lt;5}" width="5020.1" height="1008.6">

karena ada syarat akar maka:

akar 1: $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b54b2ecdb797ca4175b5c30dbf334e174b90030b" alt="{\displaystyle x^{2}-4x\geq 0}" width="5156.9" height="1223.9">$

dibuat harga nol

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec8b319def730dc7dd529e7b89021b9a22e8b6dc" alt="{\displaystyle x^{2}-4x=0}" width="5156.9" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e3e3332fa22c4b76cf2b3119193f7afc92e1f7e" alt="{\displaystyle x(x-4)=0}" width="5482" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d784c1932f75009439d80fb61e17cbfdec207e77" alt="{\displaystyle x=0\lor x=4}" width="5926.1" height="936.9">

dibuat irisan

0	4
+++	N/A	—-	N/A	+++

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6eb782b127ea48cbee3507d64b378c4b5deb6f63" alt="{\displaystyle x\leq 0\lor x\geq 4}" width="5926.1" height="1008.6">

akar 2: $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/361f0bcbfdefe9d68ac8c09a9641f6a81ad1a831" alt="{\displaystyle 10-x\geq 0}" width="4631" height="1008.6">$; $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa05a8478fd54c1f89b109b887adcc1249367568" alt="{\displaystyle x\leq 10}" width="2907.6" height="1008.6">$

gabungkan umum dan syarat

irisan	-2	(0)	(4)	5	(10)
pertama	tidak	N/A	ya	N/A	ya	N/A	ya	N/A	tidak	N/A	tidak
kedua	ya	N/A	ya	N/A	tidak	N/A	ya	N/A	ya	N/A	ya
ketiga	ya	N/A	ya	N/A	ya	N/A	ya	N/A	ya	N/A	tidak

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cce90a51660dfe39fd15e1cddfff07a488ebc91c" alt="{\displaystyle HP=\{x|-2&lt;x\leq 0\lor 4\leq x&lt;5,x\in R\}}" width="18644.4" height="1223.9">

Tentukan nilai x dari pertidaksamaan $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd0d71e09c45d050915b0188004e8a1ee39afe5c" alt="{\displaystyle {\sqrt {x^{2}-4}}\geq {\sqrt {3x+50}}}" width="9214.9" height="1510.9">$ !

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd0d71e09c45d050915b0188004e8a1ee39afe5c" alt="{\displaystyle {\sqrt {x^{2}-4}}\geq {\sqrt {3x+50}}}" width="9214.9" height="1510.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5a5b127a6cbc859e1fa61b8d17aca39f003e2d3f" alt="{\displaystyle ({\sqrt {x^{2}-4}})^{2}\geq ({\sqrt {3x+50}})^{2}}" width="11680.7" height="1510.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01b01646f645fc562a010a5e2a138042c97b1e64" alt="{\displaystyle x^{2}-4\geq 3x+50}" width="7380.9" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8270fe20604f7bfcd451e4fec70a1729d3e32b2" alt="{\displaystyle x^{2}-3x-54\geq 0}" width="7380.9" height="1223.9">

dibuat harga nol

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ac3bb732c0630688cf248aa1606d818b1537a35" alt="{\displaystyle x^{2}-3x-54=0}" width="7380.9" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb4bfa80e456d2c1bb7695dfffce293a1f6a18e4" alt="{\displaystyle (x+6)(x-9)=0}" width="7984.4" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a658a99fdac0db22ebcb0985602000e00d39ce91" alt="{\displaystyle x=-6\lor x=9}" width="6704.6" height="1008.6">

dibuat irisan

(-6)	(9)
+++	N/A	—-	N/A	+++

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f4a541904765aefb78ff6a53af4253bccde0cf67" alt="{\displaystyle x\leq -6\lor x\geq 9}" width="6704.6" height="1008.6">

karena ada syarat akar maka:

akar 1: $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2db648c69ed20efa5d9bd97c23b0eb88a474b2bc" alt="{\displaystyle x^{2}-4\geq 0}" width="4584.4" height="1223.9">$

dibuat harga nol

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2648a4914598f205c3de5c39c6736b27dc7aea6" alt="{\displaystyle x^{2}-4=0}" width="4584.4" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db17eaa8f7c1f1e4618e8c9279ac28d4b7c59f0d" alt="{\displaystyle (x+2)(x-2)=0}" width="7984.4" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d0f99f10054a07742da8eedca5dd4a640ba4d4f" alt="{\displaystyle x=-2\lor x=2}" width="6704.6" height="1008.6">

dibuat irisan

(-2)	(2)
+++	N/A	—-	N/A	+++

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06c12692cecdda56c73795a1924fd52b54119f27" alt="{\displaystyle x\leq -2\lor x\geq 2}" width="6704.6" height="1008.6">

akar 2: $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17a525de54235a78008fae527a4498a4f5f0458a" alt="{\displaystyle 3x+50\geq 0}" width="5131.5" height="1008.6">$; $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73d3257479c63445a14a1ff6ac36aee279a1b20e" alt="{\displaystyle x\geq -{\frac {50}{3}}}" width="4046.1" height="2228.5">$

gabungkan umum dan syarat

irisan	(-50/3)	(-6)	(-2)	(2)	(9)
pertama	ya	N/A	ya	N/A	tidak	N/A	tidak	N/A	tidak	N/A	ya
kedua	ya	N/A	ya	N/A	ya	N/A	tidak	N/A	ya	N/A	ya
ketiga	tidak	N/A	ya	N/A	ya	N/A	ya	N/A	ya	N/A	ya

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82c40fc568bb12b8a2fdce046830226f098d5c74" alt="{\displaystyle HP=\{x|2&lt;x\leq 0\lor 4\leq x&lt;5,x\in R\}}" width="17421.4" height="1223.9">

4. Pertidaksamaan Pecahan

Dalam bentuk pertidaksamaan pecahan sebagai berikut:

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b679ee56bcd9ec3b6d9a59c306bab0ed5c2390e9" alt="{\displaystyle {\frac {f(x)}{g(x)}}&lt;0}" width="4096.6" height="2802.6">

atau

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b5c7c73dec54ab17c36b48611e0c79379e8818c6" alt="{\displaystyle {\frac {f(x)}{g(x)}}&gt;0}" width="4096.6" height="2802.6">

haruslah mempunyai syarat yaitu penyebut atau g(x) ≠ 0.

Tentukan nilai x dari pertidaksamaan $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a343faaf11821c3c7f417fa5c2a50f743debe127" alt="{\displaystyle {\frac {x-4}{x-3}}<{\frac {x+1}{x-2}}}" width="6645.9" height="2300.3">$ !

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a343faaf11821c3c7f417fa5c2a50f743debe127" alt="{\displaystyle {\frac {x-4}{x-3}}&lt;{\frac {x+1}{x-2}}}" width="6645.9" height="2300.3">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d43a06b33c940994dd57f2e9cc433449d297252" alt="{\displaystyle {\frac {x-4}{x-3}}-{\frac {x+1}{x-2}}&lt;0}" width="8369.4" height="2300.3">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8ca2f45f75f615a82dfec4affaac4164c761aa1" alt="{\displaystyle {\frac {(x-4)(x-2)-(x+1)(x-3)}{(x-3)(x-2)}}&lt;0}" width="15717.3" height="2802.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cadefa0f7c0b209e74e10ed67add0980e743141" alt="{\displaystyle {\frac {(x^{2}-6x+8)-(x^{2}-2x-3)}{(x-3)(x-2)}}&lt;0}" width="15067.1" height="2874.4">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6982686e91bd08c56395acc7d53345a4c069d34" alt="{\displaystyle {\frac {-4x+11}{(x-3)(x-2)}}&lt;0}" width="8344.4" height="2587.3">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19739ac2659b5d303645d0ca32d2eeb0efe4b224" alt="{\displaystyle -4x+11&lt;0}" width="5910" height="1008.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c57aa30b785c62e13d46a8ad3acb0e44c15732f" alt="{\displaystyle x&lt;{\frac {11}{4}}}" width="3267.6" height="2228.5">

karena ada syarat pecahan maka:

penyebut 1: $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e54abe336ad5f1cd6f576e8e08ec890c0f88b68f" alt="{\displaystyle x-3\neq 0}" width="4130.5" height="1152.1">$; $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/105ae2964dffa225bdc9cc70ca204102aadd06b9" alt="{\displaystyle x\neq 3}" width="2407.1" height="1152.1">$

penyebut 2: $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d1b2ded046305f4cbce37cf3ba038c4e87a0ee0" alt="{\displaystyle x-2\neq 0}" width="4130.5" height="1152.1">$; $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f4384e17526abbb09ad79572febfa861f7eab55" alt="{\displaystyle x\neq 2}" width="2407.1" height="1152.1">$

dibuat irisan

2	11/4	3
+++	N/A	—-	N/A	+++	N/A	—-

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ef532e84a5b98d5bd2b5f5e09c05c8a910f53e3" alt="{\displaystyle HP=\{x|2&lt;x&lt;{\frac {11}{4}}\lor x&gt;3,x\in R\}}" width="16447.4" height="2228.5">

Tentukan nilai x dari pertidaksamaan $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f22ee79d791f3177ab0d04a10302d765b08ecf3e" alt="{\displaystyle {\frac {x+6}{x+17}}\geq {\frac {1}{x-3}}}" width="7146.4" height="2300.3">$ !

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f22ee79d791f3177ab0d04a10302d765b08ecf3e" alt="{\displaystyle {\frac {x+6}{x+17}}\geq {\frac {1}{x-3}}}" width="7146.4" height="2300.3">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af1ea945a68c5bdcaa52862215525e5d57dad0a5" alt="{\displaystyle {\frac {x+6}{x+17}}-{\frac {1}{x-3}}\geq 0}" width="8869.9" height="2300.3">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04556ff31a9bb04e23ff8c3088c847545838f85f" alt="{\displaystyle {\frac {(x+6)(x-3)-(x+17)}{(x+17)(x-3)}}\geq 0}" width="13142.8" height="2802.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5febe773d20b853a6c3902675df6777db3ef758" alt="{\displaystyle {\frac {x^{2}+3x-18-x-17}{(x+17)(x-3)}}\geq 0}" width="11760.2" height="2802.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2632e2c2c02e90327dd2700ca2654b8298108a57" alt="{\displaystyle {\frac {x^{2}+2x-35}{(x-3)(x-2)}}\geq 0}" width="8344.4" height="2802.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d44002433463befa8a00c1e42e11808253d7c1b" alt="{\displaystyle x^{2}+2x-35\geq 0}" width="7380.9" height="1223.9">

dibuat harga nol

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42e1a0983c9f7abaf1a296909bbfac044e7e4d97" alt="{\displaystyle x^{2}+2x-35=0}" width="7380.9" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/289bf95369aafb3ebdf4c0f5bff45411ac49b3b9" alt="{\displaystyle (x+7)(x-5)=0}" width="7984.4" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/541e675dd7ee32629619fdfc26f13d14f486f43d" alt="{\displaystyle x=-7\lor x=5}" width="6704.6" height="1008.6">

(tanpa gambar irisan)

karena ada syarat pecahan maka:

penyebut 1: $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/94d0df0d87419926e3d5fce2cdf6b3d0c160ab62" alt="{\displaystyle x+17\neq 0}" width="4631" height="1152.1">$; $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12fe48c4ea6d7f73c293133a86180610d869f3c0" alt="{\displaystyle x\neq -17}" width="3686.1" height="1152.1">$

penyebut 2: $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e54abe336ad5f1cd6f576e8e08ec890c0f88b68f" alt="{\displaystyle x-3\neq 0}" width="4130.5" height="1152.1">$; $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/105ae2964dffa225bdc9cc70ca204102aadd06b9" alt="{\displaystyle x\neq 3}" width="2407.1" height="1152.1">$

dibuat irisan

-17	(-7)	3	(5)
+++	N/A	—-	N/A	+++	N/A	—-	N/A	+++

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d86243e7483af40d6ec05c256b7cd8ff35285fe" alt="{\displaystyle HP=\{x|x&lt;-17\lor -7\leq x&lt;3\lor x\geq 5,x\in R\}}" width="21163.4" height="1223.9">

5. Pertidaksamaan Mutlak

Dalam bentuk pertidaksamaan mutlak adalah sebagai berikut:

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a68e348422fe6b65e38064c9c15100e41faf093" alt="{\displaystyle |f(x)|&gt;g(x)}" width="5625.1" height="1223.9">

haruslah mempunyai dua nilai yaitu

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e543ca07c330f7c758d46eb2043cede44e47ca94" alt="{\displaystyle |f(x)|=\left\{{\begin{matrix}|f(x)|&lt;g(x),&{\mbox{maka penyelesaian}}-g(x)&lt;f(x)&lt;g(x)\\\\|f(x)|&gt;g(x),&{\mbox{maka penyelesaian}}f(x)&lt;-g(x)\lor f(x)&gt;g(x)\end{matrix}}\right.}" width="32033.2" height="4094.3">

Pertidaksamaan mutlak akan memungkinkan definit + dan – karena tidak memotong dan menyinggung sumbu y.

Tentukan nilai x dari pertidaksamaan $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4945faa25c905a7e17d7182aabdb8411b058bb9c" alt="{\displaystyle |x^{2}+x|<12}" width="5713.9" height="1367.4">$ !

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4945faa25c905a7e17d7182aabdb8411b058bb9c" alt="{\displaystyle |x^{2}+x|&lt;12}" width="5713.9" height="1367.4">

karena f(x) < g(x) maka penyelesaian -g(x) < f(x) < g(x)

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7678684cadc7e4466dc47a3fea036af102e2f4e0" alt="{\displaystyle -12&lt;x^{2}+x&lt;12}" width="8270.5" height="1223.9">

untuk $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f24a80b5c3bbf8461be747ab84e897d69d1f941c" alt="{\displaystyle -12<x^{2}+x}" width="5935.4" height="1223.9">$: $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f24a80b5c3bbf8461be747ab84e897d69d1f941c" alt="{\displaystyle -12<x^{2}+x}" width="5935.4" height="1223.9">$; $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e2e278718b2216675f0fc1ccd0b414f5c0e0c21" alt="{\displaystyle x^{2}+x+12>0}" width="6880.4" height="1223.9">$ definit +

untuk $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4990b98268747bfa16e75e2f9afad13e03044e5a" alt="{\displaystyle x^{2}+x<12}" width="5156.9" height="1223.9">$: $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4990b98268747bfa16e75e2f9afad13e03044e5a" alt="{\displaystyle x^{2}+x<12}" width="5156.9" height="1223.9">$; $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4581c53d17bb81d6f38314bbce2a971cc6fc672b" alt="{\displaystyle x^{2}+x-12<0}" width="6880.4" height="1223.9">$

dibuat harga nol

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebe2b120881d716c5962a5e7a349cbd59c3559b9" alt="{\displaystyle x^{2}+x-12=0}" width="6880.4" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68c6557dde954f00ab37be3513f550a749eed2d2" alt="{\displaystyle (x+4)(x-3)&lt;0}" width="7984.4" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8cf43ebe5dc4c1626cd3925fb78edf1ee814d130" alt="{\displaystyle x=-4\lor x=3}" width="6704.6" height="1008.6">

dibuat irisan

-4	3
+++	N/A	—-	N/A	+++

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77f6e0fd205dfdb729548b612219cc3b5ab731ec" alt="{\displaystyle -4&lt;x&lt;3}" width="5020.1" height="1008.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7cff7315f25da5b15734a8eeea2d74bd8e1e5f7c" alt="{\displaystyle HP=\{x|-4&lt;x&lt;3,x\in R\}}" width="13290.8" height="1223.9">

Tentukan nilai x dari persamaan $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64f34ceec60536edd4dc354ef5e330463893871b" alt="{\displaystyle |x^{2}-4x-12|-|7-6x|\geq 5}" width="12514.2" height="1367.4">$ !

terlebih dahulu untuk mempunyai batas-batas yang ada

untuk | x^2 – 4x – 12 |: $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00f4fb1f7e19a39fe2f5c143d969f2e4c88ed758" alt="{\displaystyle |x^{2}-4x-12|=\left\{{\begin{matrix}x^{2}-4x-12,&{\mbox{maka penyelesaian}}x^{2}-4x-12\geq 0\\\\-(x^{2}-4x-12),&{\mbox{maka penyelesaian}}x^{2}-4x-12<0\end{matrix}}\right.}" width="32510.5" height="4094.3">$

batasan f(x): $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cba4a6066b3fc69417bc86a2f23a0814203df3b4" alt="{\displaystyle x^{2}-4x-12\geq 0}" width="7380.9" height="1223.9">$

dibuat harga nol

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b5e012ce99f3f7903e30bc89a863c5bb6e5d303" alt="{\displaystyle x^{2}-4x-12=0}" width="7380.9" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3af4278839dcbd5b259fb9eac202369553640d91" alt="{\displaystyle (x+2)(x-6)=0}" width="7984.4" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/80839acc5e371797a799325a9fc71fe0f1e7039e" alt="{\displaystyle x=-2\lor x=6}" width="6704.6" height="1008.6">

dibuat irisan

-2	6
+++	N/A	—-	N/A	+++

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7596b74889c6f268acd0300c537b3b6ed267bd04" alt="{\displaystyle x\leq -2\lor x\geq 6}" width="6704.6" height="1008.6">

batasan -f(x): $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ccb825e7668362345afed7614fc6ae910f109433" alt="{\displaystyle x^{2}-4x-12<0}" width="7380.9" height="1223.9">$

dibuat harga nol

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b5e012ce99f3f7903e30bc89a863c5bb6e5d303" alt="{\displaystyle x^{2}-4x-12=0}" width="7380.9" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3af4278839dcbd5b259fb9eac202369553640d91" alt="{\displaystyle (x+2)(x-6)=0}" width="7984.4" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/80839acc5e371797a799325a9fc71fe0f1e7039e" alt="{\displaystyle x=-2\lor x=6}" width="6704.6" height="1008.6">

dibuat irisan

-2	6
+++	N/A	—-	N/A	+++

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cda7171deb18e8ef3b40eb5027004f2293f42453" alt="{\displaystyle -2&lt;x&lt;6}" width="5020.1" height="1008.6">

untuk | 7 – 6x |: $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c11d31773a697e7a441960395c1b284ec870c9c4" alt="{\displaystyle |7-6x|=\left\{{\begin{matrix}7-6x,&{\mbox{maka penyelesaian}}7-6x\geq 0\\\\-(7-6x),&{\mbox{maka penyelesaian}}7-6x<0\end{matrix}}\right.}" width="24261" height="4094.3">$

batasan f(x): $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5ab281b78bd9ef81aef98b21aaba426ec929993" alt="{\displaystyle 7-6x\geq 0}" width="4631" height="1008.6">$; $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/865e0385f41494a5ba1440be23abb35a1be601e4" alt="{\displaystyle x\leq {\frac {7}{6}}}" width="2767.1" height="2228.5">$

batasan -f(x): $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38199b9a3023ddff382d75aa3c2fd14b3d9443cd" alt="{\displaystyle 7-6x<0}" width="4631" height="1008.6">$; $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a4eeb2ef847f55f7f2e0b851337b8c283cfb7b3" alt="{\displaystyle x>{\frac {7}{6}}}" width="2767.1" height="2228.5">$

keempat batas-batas akan dibuat irisan

irisan	-2	7/6	6
pertama	x^2 – 4x – 12	N/A	N/A	N/A	x^2 – 4x – 12
kedua	N/A	-(x^2 – 4x – 12)	N/A	-(x^2 – 4x – 12)	N/A
ketiga	7 – 6x	N/A	7 – 6x	N/A	N/A
keempat	N/A	N/A	-(7 – 6x)	N/A	-(7 – 6x)

untuk x <= -2

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61a7a3dc1d46c784a386f194bc5e1c082b6a5a1d" alt="{\displaystyle x^{2}-4x-12-(7-6x)\geq 5}" width="12179.2" height="1367.4">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c2adae9a3edb775dc53e4f7303c23d446afc85aa" alt="{\displaystyle x^{2}-4x-12-7+6x-5\geq 0}" width="13123.7" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85bc6d4782f8c4a3a419557292591ea3075f7ed5" alt="{\displaystyle x^{2}+2x-24\geq 0}" width="7380.9" height="1223.9">

dibuat harga nol

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3561b384e9756ec1358c6376e77a47593114663b" alt="{\displaystyle x^{2}+2x-24=0}" width="7380.9" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c9866552048b3cb0077d0932977f5dc1d2025cf" alt="{\displaystyle (x+6)(x-4)=0}" width="7984.4" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf33f658e73fc36679e98a90df8500489c927bde" alt="{\displaystyle x=-6\lor x=4}" width="6704.6" height="1008.6">

dibuat irisan

(-6)	(-2)	(4)
Ya	N/A	Ya	N/A	Tidak	N/A	Tidak
+++	N/A	—-	N/A	—-	N/A	+++

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33d5427391a5c204bf187e95d4cd3ee1ca65ab29" alt="{\displaystyle x\leq -6}" width="3185.6" height="1008.6">

untuk -2 < x <= 7/6

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd434d0fe14300361e74bb8931134710c77ed511" alt="{\displaystyle -(x^{2}-4x-12)-(7-6x)\geq 5}" width="13736.7" height="1367.4">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/459d140eeebfe2316af83d88d56d1554d061b4e4" alt="{\displaystyle -x^{2}+4x+12-7+6x-5\geq 0}" width="13902.2" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/26a308950cdd0df553923bee91755cae73c3a9ed" alt="{\displaystyle x^{2}-10x\leq 0}" width="5657.4" height="1223.9">

dibuat harga nol

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/889142d737cf93d588b6a58acf05aed23291ae9f" alt="{\displaystyle x^{2}-10x=0}" width="5657.4" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a045ae2e62d629fa6c4cb582355a28a1953a769" alt="{\displaystyle x(x-10)=0}" width="5982.5" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/361fac235ab86b3ee8a42739884f1a027d6d9d75" alt="{\displaystyle x=0\lor x=10}" width="6426.6" height="936.9">

dibuat irisan

-2	(0)	(7/6)	(10)
Tidak	N/A	Ya	N/A	Ya	N/A	Tidak	N/A	Tidak
+++	N/A	+++	N/A	—-	N/A	—-	N/A	+++

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40f3d7293d2473e4302106b9d3251fee2db4aa40" alt="{\displaystyle 0\leq x\leq {\frac {7}{6}}}" width="4601.6" height="2228.5">

untuk 7/6 < x < 6

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/655374f70e7465ad111e698d0369abaf375de0fe" alt="{\displaystyle -(x^{2}-4x-12)-(-(7-6x))\geq 5}" width="15294.2" height="1367.4">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b98bba3181a905ea4c6a004fb2a87f87397f5f7" alt="{\displaystyle -x^{2}+4x+12+7-6x-5\geq 0}" width="13902.2" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04715cbe7836938031f660d631c1cda3e631897f" alt="{\displaystyle x^{2}+2x\leq 0}" width="5156.9" height="1223.9">

dibuat harga nol

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6851c2a154e5f5eaa325a8010532a5a6b483d337" alt="{\displaystyle x^{2}+2x=0}" width="5156.9" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/02dbbba17837c9bdcd69f6a4aa97e600ada8e199" alt="{\displaystyle x(x+2)=0}" width="5482" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8ce6f5174104fbc1efcdaea204a4c8c3ae88521" alt="{\displaystyle x=0\lor x=-2}" width="6704.6" height="1008.6">

dibuat irisan

(-2)	(0)	7/6	6
Tidak	N/A	Tidak	N/A	Tidak	N/A	Ya	N/A	Tidak
+++	N/A	—-	N/A	+++	N/A	+++	N/A	+++

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00595c5e33692e724937fdcc8870496acce1ac74" alt="{\displaystyle \varnothing }" width="778.5" height="865.1">

untuk x >= 6

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2aa4a414518653c790d2ead0fc3e2063570fe4e" alt="{\displaystyle x^{2}-4x-12-(-(7-6x))\geq 5}" width="13736.7" height="1367.4">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a517f480cf6cd60e43b5adf7c7c013e699e4cc3e" alt="{\displaystyle x^{2}-4x-12+7-6x-5\geq 0}" width="13123.7" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78596ed6b58f9988d0d5afb70c0bc788d741b118" alt="{\displaystyle x^{2}-10x-10\geq 0}" width="7881.4" height="1223.9">

definit +

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00595c5e33692e724937fdcc8870496acce1ac74" alt="{\displaystyle \varnothing }" width="778.5" height="865.1">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e13cfe51a1517392119518e49d7cbd087187b57" alt="{\displaystyle HP=\{x|x\leq -6\lor 0\leq x\leq {\frac {7}{6}},x\in R\}}" width="16725.4" height="2228.5">

gabungkan ketiga batas-batas. jadi:

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48fda12bd220a59290b4608eb472e209dde60854" alt="{\displaystyle HP=\{x|-{\frac {11}{5}}\leq x&lt;-{\frac {4}{3}}\lor -{\frac {4}{3}}\leq x\leq 3,x\in R\}}" width="21781.9" height="2228.5">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb6cb5e3b04377f401f688b2ea6e4d0f989c6f79" alt="{\displaystyle HP=\{x|-{\frac {11}{5}}\leq x\leq 3,x\in R\}}" width="14151.3" height="2228.5">

Tentukan nilai x dari pertidaksamaan $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/249185aa2b5392673e59281792ecfd51c5cbb87f" alt="{\displaystyle |{\frac {x+4}{10-x}}|<|{\frac {1}{x-2}}|}" width="8260.4" height="2300.3">$ !

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/249185aa2b5392673e59281792ecfd51c5cbb87f" alt="{\displaystyle |{\frac {x+4}{10-x}}|&lt;|{\frac {1}{x-2}}|}" width="8260.4" height="2300.3">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c409343b73f844bdadebf62100062e3559f2d665" alt="{\displaystyle ({\frac {x+4}{10-x}})^{2}&lt;({\frac {1}{x-2}})^{2}}" width="9612.3" height="2300.3">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aea433ca14eccb766a9b086fe2a9997a748dbc23" alt="{\displaystyle ({\frac {x+4}{10-x}})^{2}-({\frac {1}{x-2}})^{2}&lt;0}" width="11335.7" height="2300.3">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65eb1305c7b806d9114610e4fa6c6e154cf03418" alt="{\displaystyle ({\frac {x+4}{10-x}}+{\frac {1}{x-2}})({\frac {x+4}{10-x}}-{\frac {1}{x-2}})&lt;0}" width="17463.2" height="2300.3">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c4f074fc96edbd372e3d908c4d9e967f8affafb" alt="{\displaystyle ({\frac {(x+4)(x-2)+10-x}{(10-x)(x-2)}})({\frac {(x+4)(x-2)-(10-x)}{(10-x)(x-2)}})&lt;0}" width="25230.1" height="2802.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46ff1d1307efc0223ec45ba0890bf00f5da2464f" alt="{\displaystyle ({\frac {x^{2}+2x-8+10-x}{(10-x)(x-2)}})({\frac {x^{2}+2x-8-10+x}{(10-x)(x-2)}})&lt;0}" width="22242.9" height="2802.6">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/16d846b2a3b2c8d88b03a52ecc22b1724fcfd57b" alt="{\displaystyle ({\frac {x^{2}+x+2}{(10-x)(x-2)}})({\frac {x^{2}+3x-18}{(10-x)(x-2)}})&lt;0}" width="17413.3" height="2802.6">

akar dari $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95213cac83483e153f266eb5ed28c938598b2050" alt="{\displaystyle {\frac {x^{2}+x+2}{(10-x)(x-2)}}}" width="7010.4" height="2802.6">$: $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7aaa87e6a213e4b78e8079376dd96c10ce3e840e" alt="{\displaystyle {\frac {x^{2}+x+2}{(10-x)(x-2)}}<0}" width="8844.9" height="2802.6">$; $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/835e9e580a7467651d4bbb5c2956e17760f8646b" alt="{\displaystyle x^{2}+x+2=0}" width="6379.9" height="1223.9">$ definit +

karena ada syarat pecahan maka:

penyebut 1: $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/593aa12af024b252d25e619747b7c91c364edaf8" alt="{\displaystyle 10-x\neq 0}" width="4631" height="1152.1">$; $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bd7128acd393b1b2a2ca187fdbbc7a7f5e92217" alt="{\displaystyle x\neq 10}" width="2907.6" height="1152.1">$

penyebut 2: $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d1b2ded046305f4cbce37cf3ba038c4e87a0ee0" alt="{\displaystyle x-2\neq 0}" width="4130.5" height="1152.1">$; $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f4384e17526abbb09ad79572febfa861f7eab55" alt="{\displaystyle x\neq 2}" width="2407.1" height="1152.1">$

akar dari $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d40c74e46162cb40b67b6a41195c336297d9e5d" alt="{\displaystyle {\frac {x^{2}+3x-18}{(10-x)(x-2)}}}" width="7010.4" height="2802.6">$: $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4987bb170d88d3e0b47e51ba23a42b094329db7" alt="{\displaystyle {\frac {x^{2}+3x-18}{(10-x)(x-2)}}<0}" width="8844.9" height="2802.6">$; $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f0880a2b097cfb12d9f29c3def00b62fbba03bf" alt="{\displaystyle x^{2}+3x-18<0}" width="7380.9" height="1223.9">$

dibuat harga nol

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3754235408c8c6134814b2d2d1ecbd0bff9f18ec" alt="{\displaystyle x^{2}+3x-18=0}" width="7380.9" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3f6faa7a705935cffb4e0a7ea2aa48d235a249d" alt="{\displaystyle (x+6)(x-3)=0}" width="7984.4" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dad2257c9d1d1f031a64269626ed42eecc7e7d26" alt="{\displaystyle x=-6\lor x=3}" width="6704.6" height="1008.6">

(tanpa gambar irisan)

karena ada syarat pecahan maka:

penyebut 1: $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/593aa12af024b252d25e619747b7c91c364edaf8" alt="{\displaystyle 10-x\neq 0}" width="4631" height="1152.1">$; $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bd7128acd393b1b2a2ca187fdbbc7a7f5e92217" alt="{\displaystyle x\neq 10}" width="2907.6" height="1152.1">$

penyebut 2: $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d1b2ded046305f4cbce37cf3ba038c4e87a0ee0" alt="{\displaystyle x-2\neq 0}" width="4130.5" height="1152.1">$; $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f4384e17526abbb09ad79572febfa861f7eab55" alt="{\displaystyle x\neq 2}" width="2407.1" height="1152.1">$

dibuat irisan

-6	2*	3	10*
+++	N/A	—-	N/A	—-	N/A	+++	N/A	+++

nb: * = mempunyai 2 akar

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b783667caf844f5330c47f67314315accbefdd0" alt="{\displaystyle HP=\{x|-6&lt;x&lt;3,x\in R\}}" width="13290.8" height="1223.9">

Tentukan nilai x dari pertidaksamaan ${\displaystyle |{\sqrt {x^{2}-4x}}|\geq |{\sqrt {3x-10}}|}<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1de5f86f3859901a63206e77dda8e49bc8179e3" alt="{\displaystyle |{\sqrt {x^{2}-4x}}|\geq |{\sqrt {3x-10}}|}" width="10901.4" height="1510.9">$ !

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1de5f86f3859901a63206e77dda8e49bc8179e3" alt="{\displaystyle |{\sqrt {x^{2}-4x}}|\geq |{\sqrt {3x-10}}|}" width="10901.4" height="1510.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2726021021524c99a229c5e551224cb1b77ce494" alt="{\displaystyle ({\sqrt {x^{2}-4x}})^{2}\geq ({\sqrt {3x-10}})^{2}}" width="12253.2" height="1510.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f694677944868ca19c96e4cfa866d48a6ad43987" alt="{\displaystyle x^{2}-4x\geq 3x-10}" width="7953.4" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49bee15954856a6a76884033602278211f4bd500" alt="{\displaystyle x^{2}-7x+10\geq 0}" width="7380.9" height="1223.9">

dibuat harga nol

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c40d645cba25d5837bd90f5f75578a1f8689fb8" alt="{\displaystyle x^{2}-7x+10=0}" width="7380.9" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/576c905892a420bd6e967bb343c47335a66ee2be" alt="{\displaystyle (x-2)(x-5)=0}" width="7984.4" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f01559557045c2741f238659e39e007118ccefdd" alt="{\displaystyle x=2\lor x=5}" width="5926.1" height="936.9">

dibuat irisan

2	5
+++	N/A	—-	N/A	+++

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a34afb372aeb90d70416130ca988c4f01664ecdf" alt="{\displaystyle x\leq 2\lor x\geq 5}" width="5926.1" height="1008.6">

karena ada syarat akar maka:

akar 1: $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b54b2ecdb797ca4175b5c30dbf334e174b90030b" alt="{\displaystyle x^{2}-4x\geq 0}" width="5156.9" height="1223.9">$

dibuat harga nol

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec8b319def730dc7dd529e7b89021b9a22e8b6dc" alt="{\displaystyle x^{2}-4x=0}" width="5156.9" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e3e3332fa22c4b76cf2b3119193f7afc92e1f7e" alt="{\displaystyle x(x-4)=0}" width="5482" height="1223.9">

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d784c1932f75009439d80fb61e17cbfdec207e77" alt="{\displaystyle x=0\lor x=4}" width="5926.1" height="936.9">

dibuat irisan

0	4
+++	N/A	—-	N/A	+++

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6eb782b127ea48cbee3507d64b378c4b5deb6f63" alt="{\displaystyle x\leq 0\lor x\geq 4}" width="5926.1" height="1008.6">

akar 2: $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03f3dd2045694a5422528f723ca8d4a170d1a986" alt="{\displaystyle 3x-10\geq 0}" width="5131.5" height="1008.6">$; $<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68cf1cc7cf719712aef37747a99773581a9a5f55" alt="{\displaystyle x\geq {\frac {10}{3}}}" width="3267.6" height="2228.5">$

gabungkan umum dan syarat

irisan	(0)	(2)	(10/3)	(4)	(5)
pertama	ya	N/A	ya	N/A	tidak	N/A	tidak	N/A	tidak	N/A	ya
kedua	ya	N/A	tidak	N/A	tidak	N/A	tidak	N/A	ya	N/A	ya
ketiga	tidak	N/A	tidak	N/A	tidak	N/A	ya	N/A	ya	N/A	ya

<img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e8306ec84e9ca78189e7b1a8e99ee24b122d844" alt="{\displaystyle HP=\{x|x\geq 5,x\in R\}}" width="10233.3" height="1223.9">

Pertidaksamaan Matematika: Linear, Kuadrat, Akar, Pecahan, Mutlak – Contoh Soal dan Jawaban

Pertidaksamaan Matematika adalah

Notasi tanda pertidaksamaan matematika

Jenis-jenis pertidaksamaan matematika

1. Pertidaksamaan Linear

2. Pertidaksamaan Kuadrat

3. Pertidaksamaan Akar

4. Pertidaksamaan Pecahan

5. Pertidaksamaan Mutlak

untuk x >= 6

gabungkan ketiga batas-batas. jadi:

karena ada syarat pecahan maka:

dibuat harga nol

karena ada syarat pecahan maka:

dibuat irisan

dibuat harga nol

dibuat irisan

karena ada syarat akar maka:

dibuat harga nol

dibuat irisan

gabungkan umum dan syarat

Contoh Soal dan Jawaban Pertidaksamaan Matematika

1. Jika diketahui a² + b² = 1 dan c² + d² = 1. Berapa nilai minimum ac + bd – 2?

2. Nilai yang memenuhi

a)
b)
c)   atau
d)   atau
e)   atau  >

3. Himpunan titik-titik yang memenuhi pertidaksamaan `y - 2x > 0` dan `y > 4 - x` seluruhnya berada di kuadran mana?
a) I
b) II
c) I dan II
d) I dan IV
e) I, III dan IV

4. Banyaknya bilangan real a agar pertidaksamaan |x² + 2ax +3a| ≤ 2 mempunyai tepat satu solusi pada x adalah…

5. Semua nilai  yang memenuhi
a)
b)
c)
d)
e)

6. Himpunan penyelesaian dari adalah…

7. Berapa bilangan bulan terdekat dengan `y²`jika y adalah bilangan real sehingga `3 < y < 4` dan `y³ - 6y - 7 = 0?`

8. Jika `x` dan `y` memenuhi `2y² - 1` > `x` dan `9y - x + 4 = 0`, maka `x - y` memenuhi…

a)

b)

c)

d)

e)

Bacaan Lainnya

Unduh / Download Aplikasi HP Pinter Pandai

Pertidaksamaan Matematika adalah

Notasi tanda pertidaksamaan matematika

Jenis-jenis pertidaksamaan matematika

1. Pertidaksamaan Linear

2. Pertidaksamaan Kuadrat

3. Pertidaksamaan Akar

4. Pertidaksamaan Pecahan

5. Pertidaksamaan Mutlak

untuk x >= 6

gabungkan ketiga batas-batas. jadi:

karena ada syarat pecahan maka:

dibuat harga nol

karena ada syarat pecahan maka:

dibuat irisan

dibuat harga nol

dibuat irisan

karena ada syarat akar maka:

dibuat harga nol

dibuat irisan

gabungkan umum dan syarat

Contoh Soal dan Jawaban Pertidaksamaan Matematika

1. Jika diketahui a² + b² = 1 dan c² + d² = 1. Berapa nilai minimum ac + bd – 2?

3. Himpunan titik-titik yang memenuhi pertidaksamaan y - 2x > 0 dan y > 4 - x seluruhnya berada di kuadran mana? a) I b) II c) I dan II d) I dan IV e) I, III dan IV

4. Banyaknya bilangan real a agar pertidaksamaan |x² + 2ax +3a| ≤ 2 mempunyai tepat satu solusi pada x adalah…

7. Berapa bilangan bulan terdekat dengan y2 jika y adalah bilangan real sehingga 3 < y < 4 dan y3 - 6y - 7 = 0?

8. Jika x dan y memenuhi 2y2 - 1 > x dan 9y - x + 4 = 0, maka x - y memenuhi…

Bacaan Lainnya

Unduh / Download Aplikasi HP Pinter Pandai

3. Himpunan titik-titik yang memenuhi pertidaksamaan `y - 2x > 0` dan `y > 4 - x` seluruhnya berada di kuadran mana?
a) I
b) II
c) I dan II
d) I dan IV
e) I, III dan IV

7. Berapa bilangan bulan terdekat dengan `y²`jika y adalah bilangan real sehingga `3 < y < 4` dan `y³ - 6y - 7 = 0?`

8. Jika `x` dan `y` memenuhi `2y² - 1` > `x` dan `9y - x + 4 = 0`, maka `x - y` memenuhi…