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

Mar 10, 2018

x ≥ 14

#### Explanation:

$\frac{3}{4} x - \frac{2}{3} x = \frac{1}{12} x$

$- \frac{6}{4} - \frac{5}{3} = - \frac{38}{12}$

$\frac{1}{12} x - \frac{38}{12} \ge - 2$

$\frac{1}{12} x \ge - 2 + \frac{38}{12}$

$\frac{1}{12} x \ge - \frac{24}{12} + \frac{38}{12} = \frac{14}{12}$

$\frac{1}{12} x \cdot 12$

$\frac{14}{12} \cdot 12 = 14$

$x \ge 14$

Now replace x with 14 and the equality would be $- 2 \ge - 2$