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

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Answer 1 · 2015-08-17T00:43:52

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

$- 4 < x < 5$ $-4 < x < 5$

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

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

Solving each one as follows

$2 x - 1 < 9$ $2x-1 < 9$

$2 x < 10$ $2x<10$

$x < 5$ $x < 5$

Now for the next one

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

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

$2 x > - 8$ $2x > -8$

$x > - 4$ $x > -4$

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