Let's solve the equation step by step:

### Given equation:
\[
-5(2x + 2) - x - 2 = 21
\]

### Step 1: Distribute \(-5\) to the terms inside the parentheses:
\[
-5(2x) + (-5)(2) = -10x - 10
\]
So the equation becomes:
\[
-10x - 10 - x - 2 = 21
\]

### Step 2: Combine like terms on the left-hand side:
\[
-10x - x = -11x
\]
\[
-10 - 2 = -12
\]
Thus, the equation simplifies to:
\[
-11x - 12 = 21
\]

### Step 3: Add 12 to both sides to isolate the terms with \(x\):
\[
-11x - 12 + 12 = 21 + 12
\]
\[
-11x = 33
\]

### Step 4: Divide both sides by \(-11\) to solve for \(x\):
\[
x = \frac{33}{-11} = -3
\]

### Solution:
\[
x = -3
\]

Let me know if you'd like further details or have any other questions.

---

Here are 5 related questions you might find interesting:
1. How would the solution change if the constant on the right-hand side were different, e.g., 15 instead of 21?
2. What happens if the coefficient of \(x\) inside the parentheses changes, e.g., \(3x\) instead of \(2x\)?
3. How would the solution differ if the equation were \(-5(2x + 2) + x - 2 = 21\)?
4. Can you apply the distributive property in reverse to factor the original equation?
5. What would happen if the equation involved a quadratic term instead?

**Tip:** When solving equations with parentheses, always start by distributing multiplication to simplify the equation step by step.

Learn how to solve the linear equation −5(2x+2)−x−2=21 using the distributive property and basic algebraic techniques. Follow a detailed step-by-step guide suitable for students in Grades 7-9, including combining like terms and isolating variables.

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