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SAT Math skill page

SAT Absolute Value Equations Practice

Turn absolute value statements into distance relationships and check both possible cases.

Practice absolute value equations in Dolphin SATPractice questions
10-16 min practice time3 questions on pageAdvanced Math
Practice time10-16 min
Question bank3 questions
Best forAdvanced Math

What this tests

What to know for this SAT skill

Dolphin question bank

Practice your skill

Question 1 of 3Easy
If |x - 3| = 5, which value could be x?
  1. -2
  2. 1
  3. 3
  4. 5
Show answer and solution
Correct answerA. -2

Solution walkthrough

  1. The expression x - 3 is 5 units from zero, so x - 3 = 5 or x - 3 = -5.
  2. That gives x = 8 or x = -2.
Question 2 of 3Medium
If |2x + 1| = 9, what is one possible value of x?
  1. -5
  2. -4
  3. 3
  4. 9
Show answer and solution
Correct answerA. -5

Solution walkthrough

  1. Set 2x + 1 = 9 or 2x + 1 = -9.
  2. The solutions are x = 4 and x = -5.
Question 3 of 3Hard
For which equation is there no solution?
  1. |x| = 4
  2. |x - 2| = 0
  3. |x + 1| = -3
  4. |2x| = 8
Show answer and solution
Correct answerC. |x + 1| = -3

Solution walkthrough

  1. An absolute value cannot be negative, so |x + 1| = -3 has no solution.

Avoid these traps

Common mistakes on this skill

Solving only the positive case

If |expression| = k with k > 0, the expression can equal k or -k.

Keeping solutions when the absolute value equals a negative number

An absolute value cannot be negative, so |expression| = k has no solution when k < 0.

Study plan

How to practice this skill in Dolphin

  1. Isolate the absolute-value expression before splitting into cases.
  2. Write and solve both equations when the other side is positive.
  3. Substitute every candidate into the original equation and apply any domain restrictions.
Practice absolute value equations in Dolphin SAT

Related practice

Build the surrounding skills

SAT Linear Equations PracticeSAT Inequalities PracticeSAT Systems of Equations PracticeSAT Math skill hub

Skill cluster

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FAQ

Questions about SAT Absolute Value Equations Practice

Why can an absolute-value equation have two solutions?

Absolute value measures distance from zero, so a positive distance can occur on either side of zero.

When does an absolute-value equation have no solution?

It has no solution when an isolated absolute value is set equal to a negative number.