4|2x − 2| + 10 = 34
4|2x − 2| + 10 - 10 = 34 - 10
4|2x − 2| = 24
|2x − 2| = 24/4 = 6
2x - 2 = 6 or 2x - 2 = -6
2x = 6 + 2 or 2x = -6 + 2
2x = 8 or 2x = -4
x = 8/2 or x = -4/2
x = 4 or x = -2
To check for extraneous solutions:
For x = 4:
4|2(4) − 2| + 10 = 34
4|8 − 2| = 34 - 10 = 24
6 = 24/4 = 6 (solution is valid)
For x = -2:
4|2(-2) − 2| + 10 = 34
4|-4 − 2| = 34 - 10 = 24
|-6| = 6 = 24/4 = 6 (solution is valid)
Therefore, solutions are x = 4 , x = -2
