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

1 Answer
May 29, 2018

Answer:

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#