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

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Answer 1 · 2016-12-30T13:21:41

The answer is $x in [2, 4 [$

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

The domain of $f(x)$ is $D_f(x)=RR-{4}$

We have to make a sign chart

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

$color(white)(aaaa)$ $2-x$ $color(white)(aaaaaa)$ $+$ $color(white)(aaaa)$ $-$ $color(white)(aa)$ $∥$ $color(white)(aa)$ $-$

$color(white)(aaaa)$ $x-4$ $color(white)(aaaaaa)$ $-$ $color(white)(aaaa)$ $-$ $color(white)(aa)$ $∥$ $color(white)(aa)$ $+$

$color(white)(aaaa)$ $f(x)$ $color(white)(aaaaaaa)$ $-$ $color(white)(aaaa)$ $+$ $color(white)(aa)$ $∥$ $color(white)(aa)$ $-$

Therefore,

$f(x)>=0$ when $x in [2, 4 [$

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