# How do you solve # abs(8-2x)=4#?

##### 1 Answer

Oct 16, 2015

#### Explanation:

Since you're dealing with the absolute value of an expression, you know that you're going to have to take into account the fact that the absolute value of a real number returns a **positive value** *regardless* of the sign of said number.

This implies that you will have two cases, one in which the expression inside the modulus is *positive*, and the other when it's *negative*.

#8-2x >= 0 implies |8-2x| = 8-2x#

The equation takes the form

#8 - 2x = 4#

#-2x = -4 implies x = ((_4))/((-2)) = 2#

#8-2x < 0 implies |8 - 2x| = -(8 - 2x)#

This time, you have

#-(8-2x) = 4#

#-8 + 2x = 4#

#2x = 12 implies x = 12/2 = 6#