# How do you solve |x - 4|< 2?

May 29, 2018

Solution is set of values:

$2 < x < 6$

#### Explanation:

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x |$= $\pm x$

x−4<+-2

Step 1: Set up the positive portion of the $\pm$ solution.

x−4<2

Add $4$ both sides:

$x - 4 + 4 < 2 + 4$

$x < 6$

Step 2: Set up the negative portion of the $\pm$ solution. When solving the negative portion of an inequality, flip the direction of the inequality sign.

x−4>−2

Add $4$ both sides:

$x - 4 + 4 > - 2 + 4$

$x > 2$

The solution to the inequality includes both the positive and negative versions of the absolute value.

$x < 6$ and $x > 2$

Solution is set of values:

$2 < x < 6$