To solve the absolute value equation $5|2x - 5| = 25$, we can start by isolating the absolute value expression. Here's the step-by-step process:

Step 1: Isolate the absolute value expression

Divide both sides of the equation by 5: $|2x - 5| = \frac{25}{5} = 5$

Step 2: Set up the two cases for the absolute value equation

An absolute value equation $|A| = B$ implies that $A = B$ or $A = -B$. So, we have two cases:

1. Case 1: $2x - 5 = 5$
2. Case 2: $2x - 5 = -5$

Step 3: Solve each case separately

Case 1: $2x - 5 = 5$ $2x = 5 + 5 = 10$ $x = \frac{10}{2} = 5$

Case 2: $2x - 5 = -5$ $2x = -5 + 5 = 0$ $x = \frac{0}{2} = 0$

Step 4: Write the solution set

The solutions from both cases are $x = 5$ and $x = 0$.

So, the solution set is $\{0, 5\}$.

Final Answer

A. The solution set is $\{0, 5\}$.

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

Follow-up Questions:

1. What happens if the absolute value equation has a negative number on the right side?
2. How do you solve absolute value inequalities instead of equations?
3. Can an absolute value equation ever have exactly one solution? When?
4. What is the geometric interpretation of solving an absolute value equation?
5. How does the solution change if the equation was $|2x - 5| = 0$?

Tip: When solving absolute value equations, always remember to consider both the positive and negative cases.