# How do you solve 3/4(x - 2) - 1/3(5 - 2x) < -2?

##### 1 Answer
May 16, 2015

$\frac{3}{4} \left(x - 2\right) - \frac{1}{3} \left(5 - 2 x\right) < - 2$

Multiply both sides by 12 to get

$9 \left(x - 2\right) - 4 \left(5 - 2 x\right) < - 24$

Now

$9 \left(x - 2\right) - 4 \left(5 - 2 x\right)$

$= 9 x - 9 \cdot 2 - 4 \cdot 5 - 4 \left(- 2 x\right)$

$= 9 x - 18 - 40 + 8 x$

$= 17 x - 58$

So

$17 x - 58 < - 24$

Add 58 to both sides to get

$17 x < 34$

Divide both sides by 17 to get

$x < 2$

With inequalities you can perform any of the following operations while preserving the truth of the inequality:

(1) Add or subtract the same value on both sides.
(2) Multiply or divide both sides by the same positive value.
(3) Multiply or divide both sides by the same negative value and reverse the inequality.