Question

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

Answer 1

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

Explanation:

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[`