The equation given in the image is:

$|5 - 2x| = 4$

To solve this absolute value equation, we will split it into two cases:

Case 1: Positive case

In the first case, we remove the absolute value and solve the equation directly: $5 - 2x = 4$ Subtract 5 from both sides: $-2x = -1$ Now, divide both sides by -2: $x = \frac{-1}{-2} = \frac{1}{2}$

Case 2: Negative case

In the second case, we negate the right side of the equation and solve: $5 - 2x = -4$ Subtract 5 from both sides: $-2x = -9$ Now, divide both sides by -2: $x = \frac{-9}{-2} = \frac{9}{2}$

Final Solution:

The solutions to the equation are: $x = \frac{1}{2} \quad \text{or} \quad x = \frac{9}{2}$

Would you like a further breakdown or have any questions?

Here are five related questions to expand on this topic:

1. How do you graph the solutions of absolute value equations?
2. What happens if the right-hand side of the absolute value equation is negative?
3. Can you explain how to solve inequalities involving absolute values?
4. How does the absolute value function behave geometrically on a number line?
5. Can absolute value equations have no solution?

Tip: Always check your solutions by substituting them back into the original equation, especially for more complex absolute value problems.