The solutions to the absolute value equation |8 - x| = 1 are x = 7 and
x = 9 after considering both possible cases.
To solve the absolute value equation |8 - x| = 1, we'll consider two cases:
Case 1: 8 - x = 1
8 - x = 1
Subtract 8 from both sides:
-x = -7
Multiply both sides by -1:
x = 7
Case 2: -(8 - x) = 1
-(8 - x) = 1
Distribute the negative sign:
-8 + x = 1
Add 8 to both sides:
x = 9
So, the solutions to the equation |8 - x| = 1 are x = 7 and x = 9. It's crucial to consider both cases when dealing with absolute value equations, as the expression within the absolute value can be either positive or negative.