How do you solve $x/(x+20)>2/(x+8)$ using a sign chart?

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How do you solve $x/(x+20)>2/(x+8)$ using a sign chart?

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Answer 1 · 2017-05-29T14:17:18

The solution is $x in (-oo,-20) uu (-10, -8) uu (4+oo)$

Explanation:

Let's rearrange the equation, we cannot do crossing over

$x/(x+20)>2/(x+8)$

$x/(x+20)-2/(x+8)>0$

The LCD is $(x+20)(x+8)$

So,

$(x(x+8)-2(x+20))/((x+20)(x+8))>0$

$(x^2+8x-2x-40)/((x+20)(x+8))>0$

$(x^2+6x-40)/((x+20)(x+8))>0$

$((x+10)(x-4))/((x+20)(x+8))>0$

Let $f(x)=((x+10)(x-4))/((x+20)(x+8))$

We can build the sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaa)$ $-20$ $color(white)(aaaa)$ $-10$ $color(white)(aaaa)$ $-8$ $color(white)(aaaaa)$ $4$ $color(white)(aaaa)$ $+oo$

$color(white)(aaaa)$ $x+20$ $color(white)(aaaaa)$ $-$ $color(white)(aa)$ $||$ $color(white)(aaa)$ $+$ $color(white)(aaaa)$ $+$ $color(white)(aa)$ $||$ $color(white)(aa)$ $+$ $color(white)(aa)$ $+$

$color(white)(aaaa)$ $x+10$ $color(white)(aaaaa)$ $-$ $color(white)(aa)$ $||$ $color(white)(aaa)$ $-$ $color(white)(aaaa)$ $+$ $color(white)(aa)$ $||$ $color(white)(aa)$ $+$ $color(white)(aa)$ $+$

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

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

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

Therefore,

$f(x)>0$ when $x in (-oo,-20) uu (-10, -8) uu (4+oo)$

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How do you solve $x/(x+20)>2/(x+8)$ using a sign chart?

1 Answer

Explanation:

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How do you solve x/(x+20)>2/(x+8)x/(x+20)>2/(x+8) using a sign chart?

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Explanation:

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How do you solve $x/(x+20)>2/(x+8)$ using a sign chart?