# How do you solve the inequality 2(x-3) <4(x+1/2)?

Nov 26, 2015

Simplify the the expression on each side; add and subtract to isolate $x$; then reverse the inequality to get
$\textcolor{w h i t e}{\text{XXX}} x > - 4$

#### Explanation:

$2 \left(x - 3\right) < 4 \left(x + \frac{1}{2}\right)$

Expand the expression on each side:
$2 x - 6 < 4 x + 2$

Subtract $\left(2 x + 2\right)$ from both sides
(you can always subtract the same amount from both sides of an inequality with out effecting the validity or orientation of the inequality)
$- 8 < 2 x$

Divide both sides by $2$
(you can always multiply or divide by any amount $> 0$ without effecting the validity or orientation of the inequality)
$- 4 < x$

Reversal of inequality (doesn't really change it but makes it look more standard)
$x > - 1$