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Absolute Value
Lesson 2
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Lesson 2: Absolute Value Equations

Treat absolute value as distance from zero.

Absolute value measures distance. Equations with absolute value usually split into two linear cases because distance can come from both directions.

Key formula

∣x−h∣=d⇒x=h±d|x-h|=d\Rightarrow x=h\pm d

Worked example

∣x−−8∣=1⇒x∈{−9,−7}|x--8|=1\Rightarrow x\in\left\{-9,-7\right\}

Checkpoint

Greater solution of ∣x−0∣=5 is ?\text{Greater solution of }|x-0|=5\text{ is }?

Recap

  • - Absolute value captures distance, never negative by itself.
  • - Most equations split into two linear branches.
  • - Inequalities create interval-style results.
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