Let's solve the equation step by step.

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

### Step 1: Distribute \(-5\) across \((2x + 2)\)
\[
-5(2x + 2) = -10x - 10
\]
Now, substitute this back into the equation:
\[
-10x - 10 - x - 2 = 21
\]

### Step 2: Combine like terms
\[
-10x - x = -11x \quad \text{and} \quad -10 - 2 = -12
\]
So the equation becomes:
\[
-11x - 12 = 21
\]

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

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

Thus, the solution is:
\[
x = -3
\]

Would you like further details or explanations?

Here are 5 related questions:
1. How do you handle equations with multiple variables?
2. What is the difference between distributing and factoring in algebra?
3. Can you explain the concept of like terms?
4. How can you solve equations involving fractions?
5. What happens if an equation has no solution?

**Tip:** Always distribute first when dealing with parentheses before combining like terms in an equation.

Learn how to solve the linear equation −5(2x+2)−x−2 = 21 with a step-by-step solution. This problem covers key algebraic concepts such as the distributive property and combining like terms. Suitable for students in Grades 6-8.

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