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Year 10 · Patterns & Algebra

Absolute value equations

Absolute value is distance from zero, so it is never negative: |−5| = 5. Equations with it have two cases.

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How to do it

  1. |x − a| = b means x − a = b or x − a = −b.
  2. Solve both.

Worked example

Solve |x + 4| = 2
The inside is either 2 or −2: x − (-4) = 2 gives -2; x − (-4) = −2 gives -6.
Answer: x = -2 or x = -6

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Two solutions, not one.

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