MathAbsolute Value Equations

Course Outline
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Study GuideMathAbsolute Value Equations
🔢 Algebra~35% of SAT Math

Absolute Value Equations

Solve equations and inequalities involving absolute value.

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Worked Example

Practice Problems

Problem

|x - 3| = 7

Problem

2|x + 1| - 3 = 5

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SAT Strategies

Pro Tips & Shortcuts

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SAT Tip: Absolute value equations often have two solutions because distance can be measured in two directions.

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SAT Tip: Most absolute value equations have 2 solutions. If you only find 1, check your work!

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SAT Tip: Set up two equations immediately when you see absolute value equals a number.

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SAT Tip: Check: |10 - 3| = |7| = 7 ✓ and |-4 - 3| = |-7| = 7 ✓

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SAT Tip: Always isolate the absolute value expression before splitting into two cases.

⚡ Shortcut

Think of |x| as asking: How far is x from zero?

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Remember: |x| = 5 means x is 5 units from zero in EITHER direction.

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Write both equations side by side to avoid forgetting one.

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Both solutions are 7 units away from 3 on the number line.

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Get |expression| = number first, then split.