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

1 Answer
May 29, 2018

Solution is set of values:

2< x< 6

Explanation:

Remove the absolute value term. This creates a +- on the right side of the equation because |x|= +-x

x−4<+-2

Step 1: Set up the positive portion of the +- solution.

x−4<2

Add 4 both sides:

x-4+4<2+4

x<6

Step 2: Set up the negative portion of the +- 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