We need to solve the equation:

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

### Step 1: Multiply both sides of the equation by 3 to eliminate the fraction
\[
x = -2 \times 3
\]
\[
x = -6
\]

So, the solution is:
\[
x = -6
\]

Would you like further clarification on any step or have other questions?

Here are 5 related questions:
1. What if the equation was \(\frac{1}{4}x = -2\)?
2. How would you solve \(\frac{2}{5}x = -3\)?
3. What happens if the right-hand side is a fraction, like \(\frac{1}{3}x = \frac{-5}{2}\)?
4. How would you check if your solution to \(\frac{1}{3}x = -2\) is correct?
5. How would the solution change if the left-hand side was \(\frac{2}{3}x = -2\)?

**Tip:** When solving equations with fractions, multiplying by the reciprocal of the fraction helps eliminate it easily.

Learn how to solve the linear equation \frac{1}{3}x = -2 with a step-by-step solution. This problem covers essential algebraic concepts such as linear equations and handling fractions. Suitable for students in Grades 6-8.

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