Find the solution set of |2x-3| + 1 = 6.

You have an absolute value equation.
First, isolate the absolute value part.
Then, turn it into two equations and solve the two equations separately.

|2x - 3| + 1 = 6

First, we isolate the absolute value expression:

|2x - 3| = 5

Now we separate the problem into two different equations and solve both equations.

2x - 3 = 5 or 2x - 3 = -5

2x = 8    or    2x = -2

x = 4      or     x = -1

x = -1 or x = 4