The equation given is:

$5 = |2x - 3|$

To solve this, we need to remove the absolute value, which leads to two cases:

Case 1: $2x - 3 = 5$

Solve for $x$: $2x - 3 = 5$ Add 3 to both sides: $2x = 8$ Divide by 2: $x = 4$

Case 2: $2x - 3 = -5$

Solve for $x$: $2x - 3 = -5$ Add 3 to both sides: $2x = -2$ Divide by 2: $x = -1$

Thus, the solutions are $x = 4$ and $x = -1$.

Looking at the choices, the closest match is the option where $x = -1, 4$, which seems to correspond to the correct solution.

Would you like further details on absolute value equations, or do you have any questions?

Here are some related questions:

1. How do you handle absolute value inequalities?
2. Can absolute value equations have no solutions?
3. What is the geometric interpretation of absolute value equations?
4. How do you verify the solutions to an absolute value equation?
5. How can you solve equations with multiple absolute value expressions?

Tip: Always check both possible cases when solving absolute value equations to ensure you capture all solutions.