Unit 1 · Lesson 12
Absolute Value Equations
Lesson Summary
Absolute value tells you how far a number is from zero. It's always positive (or zero).
Because of this, absolute value equations usually have two answers.
Example 1: |x| = 5
x = 5 or x = −5. Both are 5 units from zero.
Example 2: |x + 3| = 7
Set up two equations: x + 3 = 7 and x + 3 = −7
Solve each: x = 4 and x = −10
Example 3: |x − 4| + 3 = 10
First, get the absolute value by itself: |x − 4| = 7
Then set up two equations: x − 4 = 7 and x − 4 = −7
Solve each: x = 11 and x = −3
Example 4: |x + 2| = −5
No solution! Absolute value can never be negative.