Question

Solve for x: 4|2x − 2| + 10 = 34.

Answer 1

Your answer would be X=4,-2

Answer 2

Remark
This will have 2 solutions. I will enclose a graph to show how it is done.
4|2x - 2| + 10 = 34 Subtract 10

Solution
4|2x - 2| = 34 - 10
4|2x - 2| = 24             Divide by 4
|2x - 2| = 24/4      
|2x - 2| = 6

Solution 1
2x - 2 = 6                  Add 2
2x = 6 + 2
2x = 8                        Divide by 2
x = 8/2
x = 4

Solution 2
Make the 6 into - 6 and solve again
|2x - 2| = - 6
2x - 2= -6                  Add 2 to both sides.
2x  = - 6 + 2
2x = - 4                     Divide by 2
x = - 4/2
x = - 2

Answer
There are 2 solutions 
(-2,0) and (4,0) See the graph below.