# How do you solve the inequality 5x < 2x - 6?

Nov 23, 2016

$\textcolor{g r e e n}{x < - 2}$

#### Explanation:

Remember that given an inequality:
[1]$\textcolor{w h i t e}{\text{XXX}}$ you can add or subtract the same amount to/from both sides, and
[2]$\textcolor{w h i t e}{\text{XXX}}$ you can multiply or divide both sides by any positive amount
without changing the validity or direction of the inequality.

Given:
$\textcolor{w h i t e}{\text{XXX}} \textcolor{g r e e n}{5 x < 2 x - 6}$

We can subtract $\textcolor{g r e e n}{2 x}$ from both sides to get:
$\textcolor{w h i t e}{\text{XXX}} \textcolor{g r e e n}{3 x < - 6}$

Then, if we divide both sides by $\textcolor{g r e e n}{3}$
$\textcolor{w h i t e}{\text{XXX}} \textcolor{g r e e n}{x < - 2}$