Chapter A.9, Problem 104AYU

To determine

To express: The fact that $x$ differs from 2 by more than 3 as an inequality involving an absolute value. Solve for x.

Answer to Problem 104AYU

$\left\{x|x < -1 or x > 5\right\}\text{ or }\left(-\infty , -1\right) \cup \left(5, \infty \right)$

Explanation of Solution

$\begin{array}{l}|x-2| > 3\hfill \\ x - 2 < -3\text{ or }x - 2 > 3\hfill \\ x - 2 + 2 < - 3 + 2\text{ or }x-2 + 2 > 3 + 2\hfill \\ x < -1\text{ or }x > 5\hfill \end{array}$

The solution set is $\left\{x|x < -1 or x > 5\right\}$ or using interval notation, all numbers in the interval $\left(-\infty , -1\right) \cup \left(5, \infty \right)$.