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!