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To solve the equation \(-2(x + 3) + 1 = -7\) for \(x\), follow these steps:

1. **Distribute the \(-2\) across the parentheses:**
   \[
   -2(x + 3) = -2x - 6
   \]
   So the equation becomes:
   \[
   -2x - 6 + 1 = -7
   \]

2. **Combine like terms on the left side:**
   \[
   -2x - 5 = -7
   \]

3. **Add 5 to both sides to isolate the term with \(x\):**
   \[
   -2x = -7 + 5
   \]
   \[
   -2x = -2
   \]

4. **Divide both sides by \(-2\) to solve for \(x\):**
   \[
   x = \frac{-2}{-2} = 1
   \]

So, the solution is \(x = 1\).

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

Here are five related questions to further your understanding:

1. What is the next step if you had \(-3(x + 4) + 2 = -8\)?
2. How do you handle equations where the distribution results in both positive and negative terms?
3. What happens if, after combining like terms, the variable term is zero?
4. Can you describe how to check if your solution is correct by substituting \(x = 1\) back into the original equation?
5. How would the process change if the equation involved fractions?

**Tip:** Always perform the same operation on both sides of an equation to maintain balance.

Learn how to solve the linear equation -2(x + 3) + 1 = -7 with a detailed step-by-step solution. This problem covers key algebraic concepts, including the distributive property and properties of equality. Suitable for students in Grades 7-9.

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