How do you solve $(x-2)/(2x+5)<0$ using a sign chart?

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Answer 1 · 2016-12-27T16:51:30

The answer is $x in ] -5/2, 2[$

Let $f(x)=(x-2)/(2x+5)$

The domain of $f(x)$ is $D_f(x)=RR-{-5/2}$

Now, we can do the sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaa)$ $-5/2$ $color(white)(aaaaa)$ $2$ $color(white)(aaaa)$ $+oo$

$color(white)(aaaa)$ $2x+5$ $color(white)(aaaa)$ $-$ $color(white)(aaa)$ $∣∣$ $color(white)(aa)$ $+$ $color(white)(aaa)$ $+$

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

$color(white)(aaaa)$ $f(x)$ $color(white)(aaaaaa)$ $+$ $color(white)(aaa)$ $∣∣$ $color(white)(aa)$ $-$ $color(white)(aaa)$ $+$

Therefore,

$f(x)<0$ , when $x in ] -5/2, 2[$

How do you solve (x-2)/(2x+5)<0(x-2)/(2x+5)<0 using a sign chart?