Let's solve the equation step by step:

Given equation:

\[
\frac{5}{2}(10x - 16) = 5
\]

### Step 1: Distribute \(\frac{5}{2}\) to both terms inside the parentheses.

\[
\frac{5}{2} \times 10x - \frac{5}{2} \times 16 = 5
\]

This simplifies to:

\[
\frac{50x}{2} - \frac{80}{2} = 5
\]

\[
25x - 40 = 5
\]

### Step 2: Add 40 to both sides to isolate the term with \(x\).

\[
25x = 45
\]

### Step 3: Divide both sides by 25 to solve for \(x\).

\[
x = \frac{45}{25}
\]

\[
x = \frac{9}{5} \text{ or } 1.8
\]

So, the solution is:

\[
x = 1.8
\]

Would you like a detailed explanation or have any further questions? Here are some related questions to explore:

1. What would the solution be if the constant term on the right side were different?
2. How does distributing fractions affect the equation-solving process?
3. What if the equation were \(\frac{5}{2}(10x - 16) = 10\)?
4. How do you handle equations with variables on both sides?
5. Can you solve a similar equation but with a different fraction?

**Tip:** Always simplify the equation step by step, especially when dealing with fractions, to avoid errors.

Learn how to solve the equation 5/2(10x - 16) = 5 with a detailed step-by-step solution. This problem involves algebraic equations and fractions, focusing on distribution and solving techniques. Suitable for students in Grades 9-12.

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