# How do you solve abs(3x+2)<7?

Apr 16, 2017

$- 3 < x < \frac{5}{3}$

#### Explanation:

Inequalities of the type $| x | < a$ always have solutions of the form

$- a < x < a$

$\Rightarrow - 7 < 3 x + 2 < 7$

$\textcolor{b l u e}{\text{ Isolate " x " in the centre interval}}$

$\text{subtract 2 from ALL three intervals}$

$- 7 - 2 < 3 x \cancel{+ 2} \cancel{- 2} < 7 - 2$

$\Rightarrow - 9 < 3 x < 5$

$\text{divide ALL three intervals by 3}$

$\frac{- 9}{3} < \frac{\cancel{3} x}{\cancel{3}} < \frac{5}{3}$

$\Rightarrow - 3 < x < \frac{5}{3} \text{ is the solution}$