Math Teacher Certification Practice Exam 2026 – Your All-in-One Guide to Exam Success!

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.