How do you solve $-3/(x+7)<=-4/(x+8)$ ?

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How do you solve $-3/(x+7)<=-4/(x+8)$ ?

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Answer 1 · 2018-05-02T13:21:00

The solution is $x in (-oo, -8)uu(-7, -4]$

Explanation:

We cannot do crossing over

$-3/(x+7)<=-4/(x+8)$

$-3/(x+7)+4/(x+8)<=0$

place everything on the same denominator

$(-3(x+8)+4(x+7))/((x+7)(x+8))<=0$

$(-3x-24+4x+28)/((x+7)(x+8))<=0$

$(x+4)/((x+7)(x+8))<=0$

Let $f(x)=(x+4)/((x+7)(x+8))$

Now build a sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaaaa)$ $-8$ $color(white)(aaaaa)$ $-7$ $color(white)(aaaa)$ $-4$ $color(white)(aaaa)$ $+oo$

$color(white)(aaaa)$ $x+8$ $color(white)(aaaaaa)$ $-$ $color(white)(aaa)$ $||$ $color(white)(aa)$ $+$ $color(white)(aaaaa)$ $+$ $color(white)(aaaa)$ $+$

$color(white)(aaaa)$ $x+7$ $color(white)(aaaaaa)$ $-$ $color(white)(aaaa)$ #color(white)(aa)-# $color(white)(aa)$ $||$ $color(white)(aa)$ $+$ $color(white)(aaaa)$ $+$

$color(white)(aaaa)$ $x+4$ $color(white)(aaaaaa)$ $-$ $color(white)(aaaa)$ #color(white)(aa)-# $color(white)(aa)$ #color(white)(aaa)-# $color(white)(aa)$ $0$ $color(white)(aa)$ $+$

$color(white)(aaaa)$ $f(x)$ $color(white)(aaaaaaa)$ $-$ $color(white)(aaa)$ $||$ $color(white)(aa)$ $+$ $color(white)(aa)$ $||$ $color(white)(aa)$ $-$ $color(white)(aa)$ $0$ $color(white)(aa)$ $+$

Therefore,

$f(x)<=0$ when $x in (-oo, -8)uu(-7, -4]$

graph{-3/(x+7)+4/(x+8) [-39.84, 17.9, -6.8, 22.07]}

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How do you solve $-3/(x+7)<=-4/(x+8)$ ?

1 Answer

Explanation:

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