How do you solve $(w-6)/w<=0$ using a sign chart?

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Answer 1 · 2017-01-23T11:56:49

The answer is $x in ]0,6]$

Let $f(w)=(w-6)/w$

The domain of $f(w)$ is $D_f(w)=RR-{0}$

Let's build the sign chart

$color(white)(aaaa)$ $w$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaaa)$ $0$ $color(white)(aaaaa)$ $6$ $color(white)(aaaaaa)$ $+oo$

$color(white)(aaaa)$ $w$ $color(white)(aaaaaaaa)$ $-$ $color(white)(aa)$ $||$ $color(white)(aa)$ $+$ $color(white)(aaaa)$ $+$

$color(white)(aaaa)$ $w-6$ $color(white)(aaaaa)$ $-$ $color(white)(aa)$ $||$ $color(white)(aa)$ $-$ $color(white)(aaaa)$ $+$

$color(white)(aaaa)$ $f(w)$ $color(white)(aaaaaa)$ $+$ $color(white)(aa)$ $||$ $color(white)(aa)$ $-$ $color(white)(aaaa)$ $+$

Therefore,

$f(w)<=0$ when $x in ]0,6]$

How do you solve (w-6)/w<=0(w-6)/w<=0 using a sign chart?