# What is the solution to the inequality abs(2x-1) <9?

Aug 17, 2015

$x > - 4$ and $x < 5$

$- 4 < x < 5$

#### Explanation:

When solving an inequality with absolute value we really have
two inequalities

$2 x - 1 < 9$ and $- \left(2 x - 1\right) < 9$

Solving each one as follows

$2 x - 1 < 9$

$2 x < 10$

$x < 5$

Now for the next one

$- \left(2 x - 1\right) < 9$

$2 x - 1 > - 9$ Dividing by the negative flips the inequality sign

$2 x > - 8$

$x > - 4$