We have the equation:

$21 = | -2x + 5 |$

The absolute value equation can be split into two cases:

Case 1: Positive scenario

$-2x + 5 = 21$

Solve for $x$: $-2x = 21 - 5$ $-2x = 16$ $x = -8$

Case 2: Negative scenario

$-2x + 5 = -21$

Solve for $x$: $-2x = -21 - 5$ $-2x = -26$ $x = 13$

Final solution:

$x = -8 \quad \text{or} \quad x = 13$

Would you like more details on this solution, or do you have any questions?

---

Here are 5 related questions to expand on this topic:

1. What is the general method to solve absolute value equations?
2. Can absolute value equations have no solution?
3. How do you solve inequalities involving absolute values?
4. What is the geometric interpretation of absolute value equations?
5. How do you graph an absolute value function?

Tip: Always check for extraneous solutions when solving absolute value equations, especially in more complex scenarios.