We are given the equation:

\[
\frac{3}{4}x - \frac{1}{2} = \frac{5}{8}
\]

### Step 1: Eliminate the fractions
To clear the fractions, we can multiply every term by the least common denominator (LCD) of the denominators. The denominators are 4, 2, and 8, and their LCD is 8.

\[
8 \times \left(\frac{3}{4}x\right) - 8 \times \left(\frac{1}{2}\right) = 8 \times \left(\frac{5}{8}\right)
\]

This simplifies to:

\[
6x - 4 = 5
\]

### Step 2: Solve for \( x \)
Now, solve the equation for \( x \):

\[
6x = 5 + 4
\]

\[
6x = 9
\]

\[
x = \frac{9}{6}
\]

\[
x = \frac{3}{2}
\]

Thus, the solution is \( x = \frac{3}{2} \).

Would you like further details or explanations? 

Here are five related questions:
1. How do you find the least common denominator?
2. What are the steps to solve a linear equation with fractions?
3. How do you simplify fractions in equations?
4. How do you verify the solution of an equation?
5. What happens if you multiply both sides of an equation by a fraction?

**Tip:** Always check your solution by substituting the value of \( x \) back into the original equation!

Learn how to solve the linear equation 3/4x - 1/2 = 5/8 with a detailed step-by-step solution. This problem covers key algebraic concepts like eliminating fractions using the least common denominator (LCD) and solving linear equations. Suitable for students in Grades 6-8.

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