To solve the equation \( \frac{5}{8} = x + \frac{9}{4} \), follow these steps:

### Step 1: Eliminate the fraction on the right-hand side.
First, rewrite the equation:

\[
x + \frac{9}{4} = \frac{5}{8}
\]

Now, subtract \( \frac{9}{4} \) from both sides:

\[
x = \frac{5}{8} - \frac{9}{4}
\]

### Step 2: Find a common denominator.
To subtract these fractions, find a common denominator. The least common denominator between 8 and 4 is 8, so rewrite \( \frac{9}{4} \) as \( \frac{18}{8} \):

\[
x = \frac{5}{8} - \frac{18}{8}
\]

### Step 3: Subtract the fractions.
Now, subtract the numerators:

\[
x = \frac{5 - 18}{8} = \frac{-13}{8}
\]

So, the solution is:

\[
x = \frac{-13}{8}
\]

Or in decimal form:

\[
x = -1.625
\]

Would you like more details or clarification on any part of this solution?

### Related Questions:
1. How do you add and subtract fractions with different denominators?
2. Can you explain how to convert improper fractions to mixed numbers?
3. How do you handle equations involving decimals instead of fractions?
4. What are some methods to solve linear equations with fractions?
5. How do you verify the solution to a fractional equation?

**Tip:** When subtracting fractions, always find the least common denominator to simplify the calculation.

Learn how to solve the linear equation 5/8 = x + 9/4 step-by-step. This guide explains key concepts like fraction subtraction and finding the least common denominator. Perfect for students in Grades 6-8 looking to improve their algebra skills.

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