Exploring Absolute Value Inequalities

An inequality with at least one absolute value expression

An equation with no absolute value expression

A compound inequality with no absolute value

A linear equation

No solution

All real numbers whose distance from 0 is more than 6

All real numbers whose distance from 0 is less than 6

All real numbers

-6 < x < 6

x = 6

x < -6 or x > 6

x = -6

No solution

All real numbers whose distance from 0 is less than 6

All real numbers whose distance from 0 is more than 6

All real numbers

x < -6 or x > 6

x = -6

-6 < x < 6

x = 6

All real numbers

No solution

x = 6

x = -6

x < -3 or x > 3

x = 5

x = -5

2 ≤ x ≤ 8

Add 5 to both sides

Isolate the absolute value term

Multiply both sides by 2

Subtract 5 from both sides

All real numbers

x = -3

No solution

x = 3

All real numbers whose distance from -6 is less than 1

All real numbers whose distance from -6 is more than 1

No solution

All real numbers