Question

Part 1: Show the work to solve |3x – 2| < 7
Part 2: Describe the graph of the solution in words.

Answer 1

You need to break the inequality into two parts.

1) Suppose 3x - 2 > 0, i.e., x > 3/2. Then
3x - 2 < 7
hence
3x < 9
or
x < 3
Thus 3/2 < x < 3

2) Now suppose 3x - 2 =< 0, i.e., x =< 3/2. Then ...

Answer 2

3x-2<7
+2 +2
3x<9
/3 /3
x<3

then negative:
-(3x-2)<7
/-1 /-1
3x-2>6 (switch signs)
+2 +2
3x>6
/3 /3
x>2


so the answers are x<3 and x>2