How do you solve $(x(4-x))/(x+2)>=0$ using a sign chart?

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How do you solve $(x(4-x))/(x+2)>=0$ using a sign chart?

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Answer 1 · 2017-11-28T09:37:11

The solution is $x in (-oo, -2) uu [0, 4]$

Explanation:

Let

$f(x)=(x(4-x))/(x+2)$

Let's build the sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaaa)$ $-2$ $color(white)(aaaaaa)$ $0$ $color(white)(aaaaaa)$ $4$ $color(white)(aaaaa)$ $+oo$

$color(white)(aaaa)$ $x+2$ $color(white)(aaaaaa)$ $-$ $color(white)(aa)$ $||$ $color(white)(aaa)$ $+$ $color(white)(aaaa)$ $+$ $color(white)(aaaaa)$ $+$

$color(white)(aaaa)$ $x$ $color(white)(aaaaaaaaaa)$ $-$ $color(white)(aa)$ $||$ $color(white)(aa)$ $-$ $color(white)(aa)$ $0$ $color(white)(aa)$ $+$ $color(white)(aaaaa)$ $+$

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

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

Therefore,

$f(x)>=0$ when $x in (-oo, -2) uu [0, 4]$

graph{(x(4-x))/(x+2) [-38.63, 43.6, -7.9, 33.2]}

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How do you solve $(x(4-x))/(x+2)>=0$ using a sign chart?

1 Answer

Explanation:

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How do you solve (x(4-x))/(x+2)>=0(x(4-x))/(x+2)>=0 using a sign chart?

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How do you solve $(x(4-x))/(x+2)>=0$ using a sign chart?