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Absolute Value
Example 3

Example 3: Absolute Value Equations

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

Problem

Greater solution of x5=4 is ?\text{Greater solution of }|x-5|=4\text{ is }?

1. Recognize Pattern

xh=dx=h±d|x-h|=d\Rightarrow x=h\pm d

2. Apply Method

x5=7x{2,12}|x-5|=7\Rightarrow x\in\left\{-2,12\right\}

3. Conclude

x=5±4x{1,9}x=5\pm4\Rightarrow x\in\left\{1,9\right\}

Final answer

x=5±4x{1,9}x=5\pm4\Rightarrow x\in\left\{1,9\right\}