Solving Absolute Value Inequalities

The absolute value for example is
| 2x – 3 | > 5 . Absolute value means the distance of X from zero. Two cases when you solve an inequality with absolute value are less than and greater than

This is the pattern for greater than
| 2x – 3 | > 5
2x – 3 < –5 or 2x – 3 > 5
2x < –2 or 2x > 8
x < –1 or x > 4

This is the pattern for less than
| 2x + 3 | < 6
–6 < 2x + 3 < 6
–6 – 3 < 2x + 3 – 3 < 6 – 3
–9 < 2x < 3
–9/2 < x < 3/2