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The equation provided is:

\[
-5y + 6 = -12y + 62
\]

To solve for \( y \), let's go through the steps.

1. **Add \(12y\) to both sides** to move all terms involving \( y \) to one side:
\[
-5y + 12y + 6 = 62
\]
\[
7y + 6 = 62
\]

2. **Subtract 6 from both sides** to isolate the \( y \)-term:
\[
7y = 62 - 6
\]
\[
7y = 56
\]

3. **Divide by 7** to solve for \( y \):
\[
y = \frac{56}{7} = 8
\]

So, the solution is:
\[
y = 8
\]

Would you like any further details or clarification? Here are 5 related questions that might interest you:

1. How would the equation change if the constant on the right side were negative?
2. What if the equation had fractional coefficients?
3. How do you verify the solution by plugging it back into the original equation?
4. How would you solve this equation graphically?
5. How does solving for \( y \) change if the coefficients are complex numbers?

**Tip:** Always perform a quick check by substituting the solution back into the original equation to ensure accuracy.

Learn how to solve the linear equation -5y + 6 = -12y + 62 with a detailed step-by-step solution. This problem covers key algebraic concepts, including simplifying expressions and solving for variables. Suitable for students in Grades 6-8.

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