Example 8: Absolute Value Equations

Absolute Value

Example 8

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

Problem

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

1. Recognize Pattern

|x-h|=d\Rightarrow x=h\pm d

2. Apply Method

|x-4|=1\Rightarrow x\in\left\{3,5\right\}

3. Conclude

x=7\pm7\Rightarrow x\in\left\{0,14\right\}

Final answer

x=7\pm7\Rightarrow x\in\left\{0,14\right\}