Question

solve for x
|x - 6| + 4 = 10
options:
x = 3 and x = -3
x = 12 and x = 0
no solution
x = -12 and x = 0

Explanation:

Step1: Isolate the absolute value

Subtract 4 from both sides: $|x - 6| + 4 - 4 = 10 - 4$ → $|x - 6| = 6$

Step2: Solve the absolute value equation

Case 1: $x - 6 = 6$ → $x = 6 + 6 = 12$
Case 2: $x - 6 = -6$ → $x = -6 + 6 = 0$

Answer:

x = 12 and x = 0 (corresponding to the option "x = 12 and x = 0")