How do you solve $-2/(x-10)<0$ using a sign chart?

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Answer 1 · 2017-03-03T16:59:08

The answer is $x in ]10,+oo[$

We rearrange the equation

$-2/(x-10)<0$

$2/(x-10)>0.$

Let $f(x)=2/(x-10$

The time chart is

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaaaaa)$ $10$ $color(white)(aaaaaaa)$ $+oo$

$color(white)(aaaa)$ $x-10$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $||$ $color(white)(aaaa)$ $+$

$color(white)(aaaa)$ $f(x)$ $color(white)(aaaaaa)$ $-$ $color(white)(aaaa)$ $||$ $color(white)(aaaa)$ $+$

Therefore,

$f(x>0)$ , when $x in ]10,+oo[$

How do you solve -2/(x-10)<0-2/(x-10)<0 using a sign chart?