Let's solve the equation step by step:

Given:
\[
-3(-2x - 2) - 2x + 2 = 28
\]

### Step 1: Distribute the \(-3\)
Apply the distributive property to \(-3(-2x - 2)\):
\[
-3(-2x - 2) = 6x + 6
\]

So the equation becomes:
\[
6x + 6 - 2x + 2 = 28
\]

### Step 2: Combine like terms
Combine the \(x\) terms and the constants:
\[
(6x - 2x) + (6 + 2) = 28
\]
\[
4x + 8 = 28
\]

### Step 3: Solve for \(x\)
Subtract 8 from both sides:
\[
4x = 28 - 8
\]
\[
4x = 20
\]

Now, divide both sides by 4:
\[
x = \frac{20}{4}
\]
\[
x = 5
\]

### Final Answer:
\[
x = 5
\]

Would you like more details or explanations on any part of the solution?

Here are 5 follow-up questions to deepen your understanding:
1. How do you apply the distributive property in an expression like this?
2. What does it mean to combine like terms?
3. How can you check if your solution is correct by substituting it back into the equation?
4. What strategies are useful for solving multi-step linear equations?
5. How does subtracting or adding constants affect the equation?

**Tip**: Always check your solution by substituting it back into the original equation to verify!

Learn how to solve the linear equation −3(−2x−2)−2x+2 = 28 with a detailed step-by-step solution. This problem covers key algebra concepts like applying the distributive property and combining like terms. Suitable for students in Grades 7-8.

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