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Absolute Value
Example 4

Example 4: Absolute Value Equations

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

Problem

Greater solution of x8=7 is ?\text{Greater solution of }|x--8|=7\text{ is }?

1. Recognize Pattern

xh=dx=h±d|x-h|=d\Rightarrow x=h\pm d

2. Apply Method

x9=7x{16,2}|x--9|=7\Rightarrow x\in\left\{-16,-2\right\}

3. Conclude

x=8±7x{15,1}x=-8\pm7\Rightarrow x\in\left\{-15,-1\right\}

Final answer

x=8±7x{15,1}x=-8\pm7\Rightarrow x\in\left\{-15,-1\right\}