# How do you solve the two step inequality 4x – 6 > 6x – 20?

Nov 28, 2015

Given
$\textcolor{w h i t e}{\text{XXX}} 4 x - 6 > 6 x - 20$

Subtract $4 x$ from both sides:
$\textcolor{w h i t e}{\text{XXX}} - 6 > 2 x - 20$

Add $20$ to both sides
$\textcolor{w h i t e}{\text{XXX}} 14 > 2 x$

Divide both sides by $2$
$\textcolor{w h i t e}{\text{XXX}} 7 > x$

(If desired) reverse to a more standard form:
$\textcolor{w h i t e}{\text{XXX}} x < 7$

Rules used which relate to evaluating inequalities:
1. The validity and orientation of an inequality is maintained if you
$\textcolor{w h i t e}{\text{XXX}}$- add or subtract the same amount to both sides.
$\textcolor{w h i t e}{\text{XXX}}$-multiply or divide both sides by an amount greater than zero.
2. $\left(a > b\right) \iff \left(b < a\right)$