How do you solve #6 - 3|2x + 6| = 0#?

1 Answer
Jul 16, 2016

Answer:

This equation has 2 solutions: #-4# and #-2#

Explanation:

We start from the equation:

#6-3|2x+6|=0#

First we move number #6# on the right side:

#-3|2x+6|=-6#

Now we can divide both sides by #-3#:

#|2x+6|=2 #

Now we can change the equation with absolute value to 2 equations without absolute value. To do this we use the definition of absolute value:

#|x|={(x,x>=0),(-x,x<0):} #

Using this definition we can write that:

#2x+6=2 vv 2x+6=-2 #

Now we have to solve the two equations to get the final answer:

#2x=-4 vv 2x=-8 #

#x=-2 vv x=-4 #