Ximpledu

Absolute Value Equation

See how to solve an absolute value equation (one variable).
6 examples and their solutions.

Absolute Value

Definition

|(+)| = (+)
|0| = 0
|(-)| = (+)
The absolute value means
how big the number is.
'|  |' is the absolute value sign.
So the absolute value
ignores the (-) sign.
|(-)| = (+)

Example

|5|
Solution

Example

|-2|
Solution

Absolute Value Equation (One Variable)

Example

|x - 1| = 2
Solution

Example

|2x - 3| + 1 = 0
Solution

Absolute Value Inequality (One Variable)

Formula

|x| < a
-a < x < a

|x| > a
→ 1) x < -a
2) x > a

Example

|x - 2| < 5
Solution

Example

|2x + 1| ≥ 9
Solution