Which value of x satisfies the equation start fraction, 5, divided by, 4, end fraction, left parenthesis, x, plus, start fraction, 5, divided by, 2, end fraction, right parenthesis, equals, start fraction, 15, divided by, 8, end fraction 
4
5
​
 (x+ 
2
5
​
 )= 
8
15
​
 ?

To solve the equation 

\[
\frac{5}{4} \left( x + \frac{5}{2} \right) = \frac{15}{8},
\]

follow these steps:

### Step 1: Distribute \(\frac{5}{4}\) over the terms inside the parentheses.

\[
\frac{5}{4} \left( x + \frac{5}{2} \right) = \frac{5}{4}x + \frac{5}{4} \times \frac{5}{2} = \frac{5}{4}x + \frac{25}{8}.
\]

### Step 2: Set the equation equal to \(\frac{15}{8}\).

\[
\frac{5}{4}x + \frac{25}{8} = \frac{15}{8}.
\]

### Step 3: Subtract \(\frac{25}{8}\) from both sides.

\[
\frac{5}{4}x = \frac{15}{8} - \frac{25}{8} = \frac{-10}{8}.
\]

Simplify the right-hand side:

\[
\frac{5}{4}x = \frac{-5}{4}.
\]

### Step 4: Solve for \(x\) by multiplying both sides by \(\frac{4}{5}\).

\[
x = \frac{-5}{4} \times \frac{4}{5} = -1.
\]

### Final Answer: \(x = -1\).

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the equation change if the coefficient \(\frac{5}{4}\) was replaced by a different fraction?
2. What happens if you change the constant term \(\frac{15}{8}\)?
3. How do you solve similar equations with more complicated fractions?
4. What if the equation had decimal numbers instead of fractions?
5. How do you check if your solution to the equation is correct?

**Tip:** When solving equations with fractions, it's helpful to first simplify by clearing the fractions if possible to make calculations easier!

Which value of x satisfies the equation \(\frac{5}{4}(x + \frac{5}{2}) = \frac{15}{8}\)?

Learn how to solve the linear equation \(\frac{5}{4}(x + \frac{5}{2}) = \frac{15}{8}\) with a step-by-step breakdown. This algebra problem involves distributing fractions, simplifying equations, and solving for x. Suitable for students in Grades 8-10.

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