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

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Answer 1 · 2015-08-17T00:43:52

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

$-4 < x < 5$

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

$2x-1< 9$ and $-(2x-1)< 9$

Solving each one as follows

$2x-1 < 9$

$2x<10$

$x < 5$

Now for the next one

$-(2x-1)< 9$

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

$2x > -8$

$x > -4$

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