How to solve absolute inequality with negative signs? - |2x - 4| < -13

- |2x - 4| < -13

multiply by -1 to clear the negative sign
|2x-4| > 13 (note the direction of the negative sign reverses

-13 > 2x-4
-9/2 > x

2x-4 > 13
2x > 17
x > 17/2

x in (-inf, -9/2) U (17/2, inf)
or
all x except -9/2 ≤ x ≤ 17/2

Divide both sides by -1. When you divide or multiply by a negative, you have to switch the inequality sign.

l2x - 4l > 13

2x - 4 > 13
2x > 17
x > 17/2

2x - 4 < -13
2x < -9
x < -9/2

Just drop both leading negative signs.
An absolute value is always positive.
so x lies between -8.5 and + 8.5