Absolute Value Equations
Solve equations and inequalities involving absolute value.
Practice Problems
|x - 3| = 7
2|x + 1| - 3 = 5
Pro Tips & Shortcuts
SAT Tip: Absolute value equations often have two solutions because distance can be measured in two directions.
SAT Tip: Most absolute value equations have 2 solutions. If you only find 1, check your work!
SAT Tip: Set up two equations immediately when you see absolute value equals a number.
SAT Tip: Check: |10 - 3| = |7| = 7 ✓ and |-4 - 3| = |-7| = 7 ✓
SAT Tip: Always isolate the absolute value expression before splitting into two cases.
Think of |x| as asking: How far is x from zero?
Remember: |x| = 5 means x is 5 units from zero in EITHER direction.
Write both equations side by side to avoid forgetting one.
Both solutions are 7 units away from 3 on the number line.
Get |expression| = number first, then split.