To solve the equation:

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

### Step 1: Eliminate the denominators
Multiply both sides of the equation by 30 (which is the least common multiple of 5 and 6) to get rid of the fractions:

\[
30 \cdot \frac{V-2}{5} = 30 \cdot \frac{-1}{6}
\]

This simplifies to:

\[
6(V-2) = -5
\]

### Step 2: Distribute the 6 on the left side:

\[
6V - 12 = -5
\]

### Step 3: Add 12 to both sides to isolate the term with \(V\):

\[
6V = -5 + 12
\]

\[
6V = 7
\]

### Step 4: Divide both sides by 6:

\[
V = \frac{7}{6}
\]

Thus, the solution is:

\[
V = \frac{7}{6}
\]

Would you like more details on any step?

### Related questions:
1. How do you solve equations with fractions more generally?
2. Can you explain how to find the least common multiple (LCM)?
3. How would this process change if the equation had decimals instead of fractions?
4. What happens if the variables are in the denominator?
5. How can you check the solution to an equation like this?

**Tip:** Always multiply both sides of an equation by the least common multiple of the denominators to eliminate fractions efficiently!

Learn how to solve the linear equation with fractions V-2/5 = -1/6 using step-by-step methods. This problem involves eliminating fractions by finding the least common multiple (LCM) and applying properties of equality. Suitable for students in Grades 6-8.

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