To solve the absolute value equation $|2x - 5| = 9$, follow these steps:

Step 1: Set up two separate equations

The absolute value equation $|2x - 5| = 9$ implies that the expression inside the absolute value can be either positive or negative. Therefore, you can split this into two separate equations:

1. $2x - 5 = 9$
2. $2x - 5 = -9$

Step 2: Solve each equation

For the first equation:

$2x - 5 = 9$ Add 5 to both sides: $2x = 14$ Divide both sides by 2: $x = 7$

For the second equation:

$2x - 5 = -9$ Add 5 to both sides: $2x = -4$ Divide both sides by 2: $x = -2$

Step 3: Write the solution

The solutions to the equation $|2x - 5| = 9$ are: $x = 7 \quad \text{or} \quad x = -2$

Would you like further details or have any questions about this solution?

Here are 5 related questions to explore further:

1. How do you solve absolute value inequalities?
2. What happens when the absolute value equals a negative number?
3. How can you graph the solution to an absolute value equation?
4. How do you solve absolute value equations with more complex expressions inside?
5. Can absolute value equations have no solution?

Tip: Always remember that solving absolute value equations involves considering both the positive and negative scenarios.