MathAlgebraMedium frequency

SAT Math: Absolute Value Equations

21+ practice questions in Praczo

What you need to know

The concept, explained

  • 1

    |A| = b means A = b OR A = −b (when b ≥ 0). Split into two separate equations.

  • 2

    First isolate the absolute value expression before splitting into two cases.

  • 3

    If |A| = negative number, there is no solution (absolute value is never negative).

  • 4

    Always check solutions in the original equation.

  • 5

    Absolute value inequalities: |A| < b means −b < A < b; |A| > b means A > b OR A < −b.

Common mistakes
  • Only considering the positive case and forgetting to solve A = −b.
  • Setting |A| = b to A = b and A = −b before isolating the absolute value, which creates errors when there are other terms outside.
Try a sample question

SAT-style practice

How many solutions does |2x − 4| = 6 have?

21+ questions ready to practice

Ready to master this concept?

Praczo tracks your mastery on all 179 SAT concepts — not just broad topics. One sample question is a start; drilling to mastery is how scores move.

3-day free trial — no credit card required