How do you solve $(x-4)/(x+3)<=0$ using a sign chart?

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Answer 1 · 2016-11-12T15:04:20

The answer is $x in ]-3,4]$

As you canot divide by $0$ , therefore $x!=-3$

Let $f(x)=(x-4)/(x+3)$

let's do the sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaa)$ $-3$ $color(white)(aaaaa)$ $4$ $color(white)(aaaaa)$ $+oo$

$color(white)(aaaa)$ $x+3$ $color(white)(aaa)$ $-$ $color(white)(aaaa)$ $∣∣$ $color(white)(aa)$ $+$ $color(white)(aaaa)$ $+$

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

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

Therefore, $f(x)<=0$ $=>$ $x in ]-3,4]$
graph{(x-4)/(x+3) [-32.46, 32.46, -16.24, 16.25]}

How do you solve (x-4)/(x+3)<=0(x-4)/(x+3)<=0 using a sign chart?