To solve the equation \(-5(x - 3) - 2x - 2 = -43\), follow these steps:

### Step 1: Distribute the \(-5\) through the expression \((x - 3)\).
\[
-5(x - 3) = -5x + 15
\]
So the equation becomes:
\[
-5x + 15 - 2x - 2 = -43
\]

### Step 2: Combine like terms on the left side.
Combine \(-5x\) and \(-2x\):
\[
-7x + 15 - 2 = -43
\]
Now, combine \(15\) and \(-2\):
\[
-7x + 13 = -43
\]

### Step 3: Isolate the variable term.
Subtract 13 from both sides of the equation:
\[
-7x = -43 - 13
\]
\[
-7x = -56
\]

### Step 4: Solve for \(x\).
Divide both sides by \(-7\):
\[
x = \frac{-56}{-7}
\]
\[
x = 8
\]

So, the solution is \(x = 8\).

Would you like more details or have any questions?

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Here are 5 related questions:
1. How would the solution change if the equation was \(-5(x - 4) - 2x - 2 = -43\)?
2. What happens if we add a constant to both sides of the equation?
3. How can we verify the solution \(x = 8\) by substituting it back into the original equation?
4. What if the equation had a different coefficient, like \(-4(x - 3) - 2x - 2 = -43\)?
5. How does the solution change if the equation includes a fraction, like \(-5(x - 3) - \frac{1}{2}x - 2 = -43\)?

**Tip:** When solving linear equations, always perform operations step by step to avoid mistakes.

Learn how to solve the equation -5(x - 3) - 2x - 2 = -43 with a detailed step-by-step solution. This problem covers key algebraic concepts such as distributing through parentheses, combining like terms, isolating variables, and solving linear equations. Suitable for students in Grades 7-9.

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