Let's solve the equation step by step:

### Equation:
\[ 10(2y + 2) - y = 2(8y - 8) \]

### Step 1: Distribute the constants
Distribute the 10 on the left-hand side and the 2 on the right-hand side:

\[
10 \cdot 2y + 10 \cdot 2 - y = 2 \cdot 8y - 2 \cdot 8
\]

This simplifies to:

\[
20y + 20 - y = 16y - 16
\]

### Step 2: Combine like terms
On the left-hand side, combine the terms involving \(y\):

\[
(20y - y) + 20 = 16y - 16
\]

This simplifies to:

\[
19y + 20 = 16y - 16
\]

### Step 3: Move all terms involving \(y\) to one side
Subtract \(16y\) from both sides:

\[
19y - 16y + 20 = -16
\]

This simplifies to:

\[
3y + 20 = -16
\]

### Step 4: Solve for \(y\)
Subtract 20 from both sides:

\[
3y = -16 - 20
\]

\[
3y = -36
\]

Now, divide both sides by 3:

\[
y = \frac{-36}{3}
\]

\[
y = -12
\]

### Final answer:
\[
y = -12
\]

Would you like more details, or do you have any questions?

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Here are 5 related questions to expand on this concept:
1. How do you solve multi-variable linear equations?
2. What happens when an equation has no solution?
3. Can you solve the equation for a variable inside an absolute value function?
4. How does distributing work in more complex algebraic expressions?
5. How can you check if your solution is correct?

**Tip**: When solving equations, always simplify both sides before attempting to move terms across the equation. This makes the process easier and reduces errors.

Learn how to solve the linear equation 10(2y + 2) - y = 2(8y - 8) with a step-by-step solution. This problem involves key algebraic concepts such as the distributive property and combining like terms. Suitable for students in Grades 8-10.

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