Let's solve the equation step by step.

Given:

\[
-8(x+5) = -3x - 7 + x - 3
\]

### Step 1: Expand both sides.
On the left side, distribute \(-8\) across \((x + 5)\):
\[
-8x - 40
\]
On the right side, combine like terms \(-3x + x\):
\[
-3x + x = -2x
\]
Now, the equation becomes:
\[
-8x - 40 = -2x - 10
\]

### Step 2: Move all terms involving \(x\) to one side.
Add \(8x\) to both sides:
\[
-40 = 6x - 10
\]

### Step 3: Isolate the constant term.
Add \(10\) to both sides:
\[
-40 + 10 = 6x
\]
\[
-30 = 6x
\]

### Step 4: Solve for \(x\).
Divide both sides by 6:
\[
x = \frac{-30}{6} = -5
\]

Thus, the solution is:
\[
x = -5
\]

Would you like more details or further explanation on any step?

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Here are 5 related questions to deepen your understanding:
1. How would the equation change if you distributed \(-8\) incorrectly?
2. What happens if you add variables on both sides instead of moving them?
3. Can you solve a similar equation with different coefficients?
4. How does combining like terms on the right side simplify the process?
5. What if the equation involved fractions instead of whole numbers?

**Tip:** Always combine like terms before moving variables to simplify equations effectively!

Explore how to solve the linear equation -8(x+5) = -3x - 7 + x - 3 with a detailed step-by-step solution. This problem highlights essential algebraic concepts such as combining like terms, using the distributive property, and isolating variables. Suitable for students in Grades 8-10.

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