ANSWER and EXPLANATION
We have the absolute value inequality:
|3x - 6| + 3 < 15
First, isolate the absolute value:
|3x - 6| < 15 - 3
|3x - 6| < 12
This absolute value inequality actually means two things:
3x - 6 < 12 and 3x - 6 > -12
We have to solve those two:
3x - 6 < 12
=> 3x < 12 + 6
3x < 18
Divide through by 3:
x < 18 / 3
x < 6
3x - 6 > -12
=> 3x > -12 + 6
3x > -6
Divide through by 3:
x > -6 / 3
x > -2
So, the solution of the inequality is x < 6 and x > -2.
Let us graph this on a number line:
That is the graph.