# How do you solve 3abs(2x-7)< 15?

Apr 7, 2015

The solution is $1 < x < 6$

#### Explanation:

To solve this inequality, we have to consider the expression inside the absolute value sign twice. Once treating it as positive and next treating it as negative.

• Case 1

$3 \left(2 x - 7\right) < 15$

$6 x - 21 < 15$

$6 x < 36 \implies x < 6$

• Case 2

$3 \left(- 2 x + 7\right) < 15$

$- 6 x + 21 < 15$

$6 x - 21 > - 15$

$6 x > 6 \implies x > 1$

The solution is thus $1 < x < 6$