Question

How do you solve `\frac { 6} { x + 3} \geq \frac { 1} { x + 3}`?

Answer 1

The solution is `x in]-3,+oo[`

Explanation:

Let's rewrite the inequality

`6/(x+3)>=1/(x+3)`

`6/(x+3)-1/(x+3)>=0`

`5/(x+3)>=0`

This is a simple sign chart

`color(white)(aaaa)` `x` `color(white)(aaaaaa)` `-oo` `color(white)(aaaaaaa)` `-3` `color(white)(aaaaaaa)` `+oo`

`color(white)(aaaa)` `x+3` `color(white)(aaaaaaa)` `-` `color(white)(aaaaa)` `||` `color(white)(aaaa)` `+`

Therefore,

The solution is `x in]-3,+oo[`