We are tasked with solving the equation:

\[
-\frac{1}{3}v - \frac{6}{7} = \frac{1}{3}
\]

### Step-by-Step Solution:

1. **Isolate the variable term**:
   We want to isolate the term involving \( v \). First, let's get rid of the constant \(-\frac{6}{7}\) on the left-hand side by adding \(\frac{6}{7}\) to both sides:

   \[
   -\frac{1}{3}v = \frac{1}{3} + \frac{6}{7}
   \]

2. **Find a common denominator**:
   To add the fractions on the right-hand side, find the least common denominator (LCD) between 3 and 7, which is 21:

   \[
   \frac{1}{3} = \frac{7}{21}, \quad \frac{6}{7} = \frac{18}{21}
   \]

   Now, we can add the fractions:

   \[
   -\frac{1}{3}v = \frac{7}{21} + \frac{18}{21} = \frac{25}{21}
   \]

3. **Solve for \( v \)**:
   To get \( v \), divide both sides of the equation by \(-\frac{1}{3}\), which is equivalent to multiplying both sides by \(-3\):

   \[
   v = -3 \times \frac{25}{21} = -\frac{75}{21}
   \]

4. **Simplify the fraction**:
   The fraction \(\frac{75}{21}\) can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 3:

   \[
   v = -\frac{75 \div 3}{21 \div 3} = -\frac{25}{7}
   \]

Thus, the solution is:

\[
v = -\frac{25}{7}
\]

### Do you need more details or have any questions?

Here are some related questions you could explore:
1. How do you add fractions with different denominators?
2. How do you multiply fractions by whole numbers?
3. What is the significance of isolating the variable in equations?
4. How do you find the greatest common divisor (GCD) of two numbers?
5. How do you check if your solution to an equation is correct?

**Tip**: Always simplify fractions as much as possible to get the most concise solution!

This page provides a detailed step-by-step solution to the linear equation -1/3v - 6/7 = 1/3. Learn how to isolate the variable, add fractions, and simplify your solution. Perfect for students in Grades 8-10 studying algebraic concepts.

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