To solve the equation \( 6x = \frac{1}{6} - 3 \), follow these steps:

### Step 1: Simplify the right-hand side
Convert the constant term on the right-hand side into a fraction with a denominator of 6:

\[
\frac{1}{6} - 3 = \frac{1}{6} - \frac{18}{6} = \frac{1 - 18}{6} = \frac{-17}{6}
\]

### Step 2: Update the equation
Now the equation becomes:

\[
6x = \frac{-17}{6}
\]

### Step 3: Divide both sides by 6
To solve for \( x \), divide both sides of the equation by 6:

\[
x = \frac{\frac{-17}{6}}{6} = \frac{-17}{36}
\]

### Final answer:
\[
x = \frac{-17}{36}
\]

Would you like further clarification on any of the steps?

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Here are 5 related questions to explore:
1. How would you solve \( 5x = \frac{2}{5} - 4 \)?
2. What is the solution to \( 4x = \frac{3}{2} - 1 \)?
3. How do you handle equations involving fractions and variables?
4. How can you simplify complex fractions before solving for \( x \)?
5. What is the general method for solving linear equations?

**Tip:** Always ensure to work with common denominators when adding or subtracting fractions.

Learn how to solve the linear equation 6x = 1/6 - 3 with step-by-step instructions. This solution covers simplifying fractions and solving for x. Perfect for students in Grades 6-8, practicing algebra and linear equations.

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