Let's solve the equation:

\[
\frac{5x}{6} - \frac{1}{2} = \frac{1}{3}
\]

### Step 1: Eliminate the fractions by finding the least common denominator (LCD)
The denominators are 6, 2, and 3. The least common denominator for these is 6.

### Step 2: Multiply every term by the LCD (which is 6) to eliminate the fractions:

\[
6 \times \frac{5x}{6} - 6 \times \frac{1}{2} = 6 \times \frac{1}{3}
\]

This simplifies to:

\[
5x - 3 = 2
\]

### Step 3: Solve for \( x \)

Add 3 to both sides to isolate the term with \( x \):

\[
5x = 5
\]

Now, divide both sides by 5:

\[
x = 1
\]

### Final Answer:
\[
x = 1
\]

Would you like any details on this solution or have any questions?

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Here are some related questions:

1. How do you solve equations with more than one variable?
2. How do you handle equations with multiple fractions?
3. What are the different methods to solve linear equations?
4. How do you check if the solution to an equation is correct?
5. How can you apply this method to more complex algebraic equations?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the linear equation 5x/6 - 1/2 = 1/3 with a detailed step-by-step solution. This problem involves fractions and solving linear equations. Suitable for students in Grades 6-8.

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