How can you find the values of x in the equation |x - 5| = 3?

To find the values of (x) that satisfy the equation (|x - 5| = 3), we need to use the property of absolute values. The equation (|A| = B) implies two scenarios: (A = B) and (A = -B).

In this case, we can set up two equations based on the expression inside the absolute value:

1. (x - 5 = 3)

2. (x - 5 = -3)

For the first equation, solving (x - 5 = 3) gives us:

[

x = 3 + 5 = 8

]

For the second equation, solving (x - 5 = -3) gives us:

[

x = -3 + 5 = 2

]

Thus, the solutions to the equation (|x - 5| = 3) are (x = 2) and (x = 8). Therefore, the correct answer is the option that states (x = 2) or (x = 8), confirming the values derived from solving the absolute value equation.