Example 4: Absolute Value Equations

Absolute Value

Example 4

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

Problem

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

1. Recognize Pattern

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

2. Apply Method

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

3. Conclude

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

Final answer

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