The absolute value equation \(8 = |5 - x|\) splits into two equations:
1. \(8 = 5 - x\)
2. \(8 = -(5 - x)\)
Now, solve both equations:
For equation 1:
Subtract 5 from both sides to give: \(3 = -x\)
Multiplying both sides by -1 so it becomes: \(-3 = x\)
For equation 2:
Simplify it to \(8 = -5 + x\)
Rearrange the equation to solve for x: \(x = 8 + 5\)
This gives: \(x = 13\)
Therefore, the solutions to the equation \(8 = |5 - x|\) are \(x = -3\) and (x = 13).