Luis’s mistake lies in the first simplification. Let’s carefully analyze the steps:

1. Starting equation:
   $-2(3x - 5) = 4(x + 3) + 8$

2. Distribute $-2$ and $4$:
   $-6x + 10 = 4x + 12 + 8$
   (This part is correct so far.)

3. Combine constants on the right:
   $-6x + 10 = 4x + 20$
   (Correct.)

4. Isolate terms:
   $-6x + 10 = 4x + 20$ → Move $4x$ to the left:
   $-6x - 4x + 10 = 20$ → $-10x + 10 = 20$

Luis’s mistake happens when simplifying to:
$10 = -2x + 20$. This step is incorrect.

Correct Solution:

From $-10x + 10 = 20$:

• Subtract 10: $-10x = 10$
• Divide by $-10$: $x = -1$

Correct Answer: $x = -1$.

Do you need further details?

5 Follow-Up Questions:

1. Why does distribution matter in the initial step?
2. How do we combine constants correctly?
3. Can you explain the process of isolating variables?
4. What is the importance of verifying solutions?
5. How would errors propagate if not caught early?

Tip: Always double-check every step to avoid errors when combining or isolating terms.