We are given the equation:

$\frac{1}{2}y + 7 = \frac{1}{6}y$

Let's solve for $y$.

Step 1: Eliminate the fractions

To eliminate the fractions, multiply both sides of the equation by 6, the least common denominator of 2 and 6:

$6 \left(\frac{1}{2}y + 7\right) = 6 \cdot \frac{1}{6}y$

Simplifying both sides:

$3y + 42 = y$

Step 2: Isolate the variable $y$

Now, subtract $y$ from both sides to move all terms involving $y$ to one side:

$3y - y + 42 = 0$

Simplify:

$2y + 42 = 0$

Step 3: Solve for $y$

Subtract 42 from both sides:

$2y = -42$

Now, divide both sides by 2:

$y = -21$

Final Answer:

$y = -21$

Would you like further explanation or have any questions about the steps? Here are 5 related questions to deepen your understanding:

1. How do you find the least common denominator when working with fractions?
2. What happens if the fractions have different denominators?
3. How do you check if your solution is correct?
4. Can this method be used to solve equations with more complex fractions?
5. How would the solution change if the constant term was negative?

Tip: Always check your solution by substituting it back into the original equation to verify its correctness.