https://file.aiquickdraw.com/mathbot/file/1728263504897cbe2f97x.jpg

The given equation is:

\[
-3y + 3(4y - 1) = 1 + 4(-8 - y)
\]

Let's solve this step by step:

### Step 1: Expand both sides
First, expand the terms on both sides.

On the left side:
\[
3(4y - 1) = 12y - 3
\]
So the left side becomes:
\[
-3y + 12y - 3 = 9y - 3
\]

On the right side:
\[
4(-8 - y) = -32 - 4y
\]
So the right side becomes:
\[
1 - 32 - 4y = -31 - 4y
\]

Now the equation is:
\[
9y - 3 = -31 - 4y
\]

### Step 2: Combine like terms
Move all terms involving \( y \) to one side and constant terms to the other side.

Add \( 4y \) to both sides:
\[
9y + 4y - 3 = -31
\]
\[
13y - 3 = -31
\]

Add \( 3 \) to both sides:
\[
13y = -28
\]

### Step 3: Solve for \( y \)
Divide both sides by \( 13 \):
\[
y = \frac{-28}{13}
\]

So, the solution is:
\[
y = \frac{-28}{13}
\]

Would you like any further details on this solution?

Here are five related questions to explore:

1. What are some common strategies for solving linear equations with variables on both sides?
2. How can we verify the solution of a linear equation by substitution?
3. What types of equations can be solved using the same steps as this one?
4. What are some common errors to avoid when solving equations with parentheses and distribution?
5. How does the method of solving change if the equation contains fractions from the beginning?

**Tip:** Always check your final solution by substituting it back into the original equation to ensure correctness.

Learn how to solve the linear equation -3y + 3(4y - 1) = 1 + 4(-8 - y) step by step. This problem involves key algebraic concepts such as the distributive property and combining like terms. Suitable for students in Grades 7-10.

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