To solve the equation \( x + \frac{1}{6} = -\frac{1}{6}y \), let's follow these steps:

### Step 1: Eliminate fractions
To get rid of the fractions, multiply the entire equation by 6, the least common denominator of the fractions:

\[
6 \left( x + \frac{1}{6} \right) = 6 \left( -\frac{1}{6}y \right)
\]

Simplifying:

\[
6x + 1 = -y
\]

### Step 2: Solve for \( y \)
Now, isolate \( y \) on one side of the equation:

\[
6x + 1 = -y
\]

Multiply both sides by \( -1 \) to make \( y \) positive:

\[
y = -(6x + 1)
\]

Thus, the solution is:

\[
y = -6x - 1
\]

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How would you solve if the equation had different fractions?
2. What is the graph of the equation \( y = -6x - 1 \)?
3. How would you rewrite the equation if you had decimals instead of fractions?
4. What happens if we make \( x \) a negative number?
5. How do you check if the solution is correct?

**Tip:** Always try to eliminate fractions early in an equation to make solving easier!

Learn how to solve the linear equation x + 1/6 = -1/6y by eliminating fractions and isolating variables. This problem covers important algebraic concepts and techniques, such as multiplying by the least common denominator and rearranging equations. Suitable for students in Grades 8-10.

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