# How do you solve and graph abs(a-5)<3?

Mar 16, 2017

$2 < a < 8$

#### Explanation:

The standard form for $| x | < a$ is.

$- a < x < a$

This is used in the question here.

$\Rightarrow - 3 < a - 5 < 3$

Isolate a in the centre interval by adding 5 to ALL 3 intervals.

$\Rightarrow - 3 + 5 < a \cancel{- 5} \cancel{+ 5} < 3 + 5$

$\Rightarrow 2 < a < 8 \leftarrow \text{ is the solution}$

To show the solution on a number line place $\textcolor{b l u e}{\text{open circles}}$ at 2 and 8 to indicate that 2 and 8 are not values in the solution. If they were we use a solid circle to denote they are part of the solution.

The solution is the values $\textcolor{b l u e}{\text{between}}$ 2 and 8 which is denoted by a heavy line drawn between the 2 open circles.