To solve the equation \(\frac{1}{2}x - 9 = \frac{5}{8}x\), we will follow these steps:

### Step 1: Eliminate the fractions by finding a common denominator.
The least common denominator between \(\frac{1}{2}\) and \(\frac{5}{8}\) is 8. So, we can multiply every term in the equation by 8 to eliminate the fractions.

\[
8 \times \left(\frac{1}{2}x - 9\right) = 8 \times \left(\frac{5}{8}x\right)
\]

This simplifies to:

\[
4x - 72 = 5x
\]

### Step 2: Isolate the variable \(x\).
Subtract \(4x\) from both sides of the equation to get:

\[
-72 = x
\]

So, the solution is \(x = -72\).

### Final Answer:
\[
x = -72
\]

Would you like more details or have any questions? Here are some related questions to practice:

1. Solve \( \frac{3}{4}x - 7 = \frac{1}{2}x + 1 \).
2. Solve \( 2x - 5 = \frac{3}{4}x + 4 \).
3. Solve \( \frac{1}{3}x + 2 = \frac{2}{3}x - 5 \).
4. Solve \( \frac{7}{8}x + 4 = \frac{1}{2}x + 2 \).
5. Solve \( \frac{5}{6}x - 10 = \frac{1}{3}x + 15 \).

**Tip:** When dealing with equations involving fractions, multiplying through by the least common denominator (LCD) can simplify the problem and eliminate the fractions.

Learn how to solve the equation (1/2x) - 9 = (5/8x) step-by-step with detailed explanations. This problem involves equations with fractions and variable isolation techniques. Suitable for students in Grades 7-9.

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