# How do you solve abs(x-2)< 5?

Jul 4, 2015

Clear the absolute value according to the pattern $\left\mid x \right\mid < a = - a < x < a$. Then solve for $x$.

#### Explanation:

$\left\mid x - 2 \right\mid < 5$

Clear the absolute value according to the pattern $\left\mid x \right\mid < a = - a < x < a$.

$- 5 < x - 2 < 5$

Solve for $x$.

Add 2 to all three terms.

$- 5 + 2 < x - 2 + 2 < 5 + 2$ =

$- 3 < x < 7$