Solve the inequality Write the solution in interval notation

Solve the inequality. Write the solution in interval notation. - |2x-5|

-|2x - 5| < -19

multiply by -1 on both sides (==> the direction of the inequality changes)

==> |2x -5| > 19

==> (2x - 5) > 19 or (2x - 5) < -19 ; since |x| = x for x > 0 and |x| = - x for x < 0

==> 2x -5 + 5 > 19 + 5 or 2x -5 +5 < -19 + 5

==> 2x > 24 or 2x < -14

==> 2x/2 > 24/2 or 2x/2 < -14/2

==> x > 12 or x < -7

Hence solution is (- , -7) U (12 , )