# How do you solve #abs(4x + 7) - 2 = 29#?

##### 1 Answer

#### Explanation:

First, isolate the modulus on one side of the equation by adding

#|4x+7| - color(red)(cancel(color(black)(2))) + color(red)(cancel(color(black)(2))) = 29 + 2#

#|4x+7| = 31#

By definition, the absolute value of a real number will always be a **positive** number.

This means that you need to take into account the fact thatthe expression that's inside the modulus can be *positive* or *negative*, since both cases would produce the same value,

This means that you have

#4x+7>=0 implies |4x+7| = 4x+7#

The equation will become

#4x+7 = 31#

#4x = 24 implies x = 24/4 = color(green)(6)#

#4x+7<0 implies |4x+7| = -(4x+7)#

This time you have

#-(4x+7) = 31#

#-4x - 7 = 31#

#x = (38)/((-4)) = color(green)(-19/2)#

Your original equation will thus have two possible solutions

#x=6" "# , for which#4x+7 = 3#

and

#x = -19/2" "# , for which#4x+7 = -31#