Question

How many solutions does the following equation have?
|3x + 12| = 18 (5 points)

Answer 1

Answer: 2 solutions.

The given equation breaks down into these two equations

3x+12 = 18 and 3x+12 = -18

Basically 3x+12 equal to plus 18 and minus 18. This is due to the fact that something like |x| = 7 means x = 7 or x = -7, ie those x values are exactly seven units away from zero on the number line.

If you want to solve each equation, then

3x+12 = 18

3x = 18-12

3x = 6

x = 6/3

x = 2 is one solution

and

3x+12 = -18

3x = -18-12

3x = -30

x = -30/3

x = -10 is the other solution