Absolute Value Equations
Absolute value equations contain |x| or |expression|. To solve them, split into two cases: one positive and one negative.
What You Need to Know
Key Concept Diagram
|x| = a means x = a or x = -a (two cases)
|expression| = a: set expression equal to +a and -a and solve both
|x| = -a has no solution since absolute value is always non-negative
Graph of y = |x| produces a V-shape symmetric about the y-axis
Key Vocabulary
Absolute value
The distance of a number from zero; always non-negative
Equation
A mathematical statement that two expressions are equal
Solution
A value of the variable that makes the equation true
Cases
The two possibilities when solving an absolute value equation
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Solve |x - 3| = 5.
Question 2
How many solutions does |2x + 1| = -3 have?
Question 3
Solve |4x| = 20.
Key Concepts Summary
- ●|x| = a means x = a or x = -a (two cases)
- ●|expression| = a: set expression equal to +a and -a and solve both
- ●|x| = -a has no solution since absolute value is always non-negative
- ●Graph of y = |x| produces a V-shape symmetric about the y-axis