The equation provided in the image is:

$|2x - 9| = 4$

This is an absolute value equation, which can be solved by breaking it down into two separate equations, because $|a| = b$ implies that $a = b$ or $a = -b$.

So, we will solve:

1. $2x - 9 = 4$
2. $2x - 9 = -4$

Solving the first equation:

$2x - 9 = 4$ Add 9 to both sides: $2x = 13$ Now divide by 2: $x = \frac{13}{2} = 6.5$

Solving the second equation:

$2x - 9 = -4$ Add 9 to both sides: $2x = 5$ Now divide by 2: $x = \frac{5}{2} = 2.5$

Final Answer:

The solutions are: $x = 6.5 \quad \text{or} \quad x = 2.5$

Would you like further details or have any other questions? Here are five related questions to explore:

1. How do you solve more complex absolute value equations?
2. What happens if the absolute value is set equal to a negative number?
3. Can absolute value inequalities be solved in a similar way?
4. What are the key properties of absolute value functions?
5. How do you graph the solution for an absolute value equation?

Tip: Always check both solutions by substituting them back into the original equation to verify.