How do you solve $(x+2)/(x+5)>=1$ using a sign chart?

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Answer 1 · 2016-11-28T07:12:16

The answer is $x in ] -oo,-5 [$

Let's rewrite the equation as

$f(x)=(x+2)/(x+5)-1>=0$

$f(x)=((x+2)-(x+5))/(x+5)>=0$

$f(x)=(x+2-x-5)/(x+5)=-3/(x+5)>=0$

The domain of $f(x)$ is $D_f(x)=RR-{-5}$

Let's do the sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaa)$ $-5$ $color(white)(aaaa)$ $+oo$

$color(white)(a)$ $-(x+5)$ $color(white)(aaaa)$ $+$ $color(white)(aaaaa)$ $-$

$color(white)(aaaa)$ $f(x)$ $color(white)(aaaaa)$ $+$ $color(white)(aaaaa)$ $-$

Therefore,

$f(x>=0)$ when $x in ] -oo,-5 [$

graph{-3/(x+5) [-18.99, 6.32, -6.33, 6.33]}

How do you solve (x+2)/(x+5)>=1(x+2)/(x+5)>=1 using a sign chart?