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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 SAT Try examples
10-16 min practice time 3 examples on page Advanced Math
Practice time 10-16 min
On-page examples 3 examples
Best for Advanced Math

What this tests

What to know for this SAT skill

Practice examples

Try a few SAT-style questions

Example 1 Easy

If |x - 3| = 5, which value could be x?

  1. -2
  2. 1
  3. 3
  4. 5
Show answer and explanation

Answer: -2

The expression x - 3 is 5 units from zero, so x - 3 = 5 or x - 3 = -5. That gives x = 8 or x = -2.

Example 2 Medium

If |2x + 1| = 9, what is one possible value of x?

  1. -5
  2. -4
  3. 3
  4. 9
Show answer and explanation

Answer: -5

Set 2x + 1 = 9 or 2x + 1 = -9. The solutions are x = 4 and x = -5.

Example 3 Hard

For which equation is there no solution?

  1. |x| = 4
  2. |x - 2| = 0
  3. |x + 1| = -3
  4. |2x| = 8
Show answer and explanation

Answer: |x + 1| = -3

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

Quick drills

Practice this skill from more angles

Drill 1

Solve simple absolute value equations

Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.

Drill 2

Set up two cases from an absolute value statement

Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.

Drill 3

Identify when an absolute value equation has no solution

Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.

Drill 4

Check proposed solutions in the original equation

Pause before the answer choices, write the rule or setup you need, then check whether the question is asking for the value, the relationship, or the best-supported conclusion.

Avoid these traps

Common mistakes on this skill

Solving before naming the task

The SAT often hides the real skill inside familiar wording. Identify the rule, relationship, or question type first.

Choosing an answer that only partly fits

Many wrong answers are close. Check every condition in the question before committing.

Skipping the final check

Reread what the question asks for so you do not answer a nearby but different question.

Study plan

How to practice this skill in Dolphin

  1. Read the question and name the tested skill before looking at the choices.
  2. Write the equation, rule, or passage relationship in plain language.
  3. Eliminate answers that violate the setup or overstate the evidence.
  4. Review misses by writing the exact trap that pulled you toward the wrong answer.
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

What is the best way to practice SAT Absolute Value Equations Practice?

Start with a few focused examples, review the mistake pattern, then mix the skill into full SAT practice so you can recognize it in context.

Why does this skill matter on the SAT?

It shows up in short, high-leverage questions where one missed rule or setup can quickly cost a point.

Can Dolphin SAT help me drill this skill?

Yes. Dolphin SAT can surface targeted practice, track missed questions, and help you review the patterns that keep repeating.