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Absolute Value
Example 11

Example 11: Absolute Value Equations

Step-by-step worked example for this lesson track.

Problem

Greater solution of ∣x−−5∣=3 is ?\text{Greater solution of }|x--5|=3\text{ is }?

1. Recognize Pattern

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

2. Apply Method

∣x−−10∣=2⇒x∈{−12,−8}|x--10|=2\Rightarrow x\in\left\{-12,-8\right\}

3. Conclude

x=−5±3⇒x∈{−8,−2}x=-5\pm3\Rightarrow x\in\left\{-8,-2\right\}

Final answer

x=−5±3⇒x∈{−8,−2}x=-5\pm3\Rightarrow x\in\left\{-8,-2\right\}
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