# How do you solve the inequality 8 − 2x < 4?

Sep 8, 2015

$x > 2$

#### Explanation:

Things you can do with expressions in an inequality which maintain the inequality orientation:

• Add the same amount to each expression
• Subtract the same amount from each expression
• Divide each expression by the same amount provided the amount is greater than zero
• Multiply each expression by the same amount provided the amount is greater than zero

Things you can do with expressions in an inequality which reverse the inequality orientation.

• Divide each expression by the same amount when the amount is less than zero
• Multiply each expression by the same amount when the amount is less than zero

Given the above rules:

$\textcolor{w h i t e}{\text{XXXX}} 8 - 2 x < 4$
subtract $8$ from both sides:
$\textcolor{w h i t e}{\text{XXXX}} - 2 x < - 4$
divide both sides by $\left(- 2\right)$, which reverses orientation of inequality
$\textcolor{w h i t e}{\text{XXXX}} x > 2$