We are given the equation:

\[
\frac{2x}{3} - \frac{3}{4} = \frac{5}{6}
\]

To solve for \(x\), let's follow these steps:

### Step 1: Eliminate the fractions
We can eliminate the denominators by finding the least common denominator (LCD) of 3, 4, and 6. The LCD of 3, 4, and 6 is 12.

Multiply the entire equation by 12:

\[
12 \times \left( \frac{2x}{3} - \frac{3}{4} \right) = 12 \times \frac{5}{6}
\]

This simplifies as follows:

\[
4 \times 2x - 3 \times 3 = 2 \times 5
\]

\[
8x - 9 = 10
\]

### Step 2: Solve for \(x\)
Now, isolate \(x\):

\[
8x = 10 + 9
\]

\[
8x = 19
\]

\[
x = \frac{19}{8}
\]

### Final Answer:
\[
x = \frac{19}{8}
\]

Would you like any more details or clarifications?

Here are some related questions:
1. How do you simplify fractions in equations?
2. How do you find the least common denominator?
3. What other methods can be used to solve equations with fractions?
4. How would this process change if the equation had variables in the denominator?
5. Can you verify if \(x = \frac{19}{8}\) is the correct solution?

**Tip:** Always check your final answer by plugging it back into the original equation.

This guide explains how to solve the linear equation 2x/3 - 3/4 = 5/6. Learn the step-by-step process to eliminate fractions by finding the least common denominator and solve for x. Ideal for students in Grades 6-8 studying algebra and linear equations.

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