To solve the absolute value equation |x - 2| = 18, we can set up two separate equations.
First, we can consider the positive case:
x - 2 = 18
Solving for x, we add 2 to both sides:
x = 20
Next, we consider the negative case:
-(x - 2) = 18
Expanding the negative sign, we have:
-x + 2 = 18
Solving for x, we subtract 2 from both sides:
-x = 16
Multiplying both sides by -1 to isolate x:
x = -16
So, the solutions to the absolute value equation |x - 2| = 18 are x = 20 and x = -16.