Express the solution in interval notation?
4x - 8/x - 4 < 3
I know the answer is (-4, 4). Can someone tell me how they got it?
4x - 8/x - 4 < 3
I know the answer is (-4, 4). Can someone tell me how they got it?
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Mistake: it should be (4x-8)/(x-4)<3.
(4x-8)/(x-4)<3=>
(4x-8)/(x-4)-3<0=>
(x+4)/(x-4)<0=>
x+4>0 and x-4<0=>
-4
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(4x-8)/(x-4)<3=>
(4x-8)/(x-4)-3<0=>
(x+4)/(x-4)<0=>
x+4>0 and x-4<0=>
-4
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Looks like that answer you thought you knew is wrong but here is the solution.
4x - 8 / x - 4 < 3
4x - 7 - 8 / x < 0
4x² - 7x - 8 < 0
16x² - 28x - 32 < 0
64x² - 112x - 128 < 0
(8x - 7)² - 177 < 0
(8x - 7)² < 177
-√177 < 8x - 7 < √177
7 - √177 < 8x < 7 + √177
(7 - √177) / 8 < x < (7 + √177) / 8
4x - 8 / x - 4 < 3
4x - 7 - 8 / x < 0
4x² - 7x - 8 < 0
16x² - 28x - 32 < 0
64x² - 112x - 128 < 0
(8x - 7)² - 177 < 0
(8x - 7)² < 177
-√177 < 8x - 7 < √177
7 - √177 < 8x < 7 + √177
(7 - √177) / 8 < x < (7 + √177) / 8
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4x - 8/x - 4 < 3
4x^2 - 8 - 4x < 3x
4x^2 - 7x - 8 < 0
x = -b ± √(b^2 - 4ac) / 2a
x = (7 ± √((49 - -128)) / 8
x = (7 ± √(177) )/ 8
x ≈ (7 ± 13.3) / 8
x ≈ 2.5375 or -0.7875
4x^2 - 8 - 4x < 3x
4x^2 - 7x - 8 < 0
x = -b ± √(b^2 - 4ac) / 2a
x = (7 ± √((49 - -128)) / 8
x = (7 ± √(177) )/ 8
x ≈ (7 ± 13.3) / 8
x ≈ 2.5375 or -0.7875
1
keywords: inequality,the,rational,Solve,Solve the rational inequality