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Looking at Vincent's solution, let’s break down his steps for the equation \(-4(-3 + s) - 10 = 22\):

### Step 1: \(12 - 4s - 10 = 22\)
Vincent distributes \(-4\) to both \(-3\) and \(s\). This part is correct:
\[
-4(-3 + s) = 12 - 4s
\]
So, after distribution, the equation becomes:
\[
12 - 4s - 10 = 22
\]
This part is fine so far.

### Step 2: \(-4s + 2 = 22\)
Here, Vincent combines like terms on the left side. He subtracts \(10\) from \(12\), which is correct:
\[
12 - 10 = 2
\]
Thus, the equation becomes:
\[
-4s + 2 = 22
\]

### Step 3: \(-4s = 24\)
In this step, he subtracts \(2\) from both sides, which is also correct:
\[
-4s + 2 - 2 = 22 - 2 \quad \Rightarrow \quad -4s = 20
\]
However, Vincent writes \(-4s = 24\), which is incorrect. The correct result should be \(-4s = 20\).

### Step 4: \(s = -6\)
Here, Vincent divides both sides by \(-4\), but since the previous step was incorrect, this result is also wrong. The correct solution should be:
\[
s = \frac{20}{-4} = -5
\]

### Conclusion:
Vincent made a mistake in **Step 3**, where he incorrectly wrote \(-4s = 24\) instead of \(-4s = 20\). Therefore, the correct answer to the question is:

**C. In Step 3, he did not add/subtract from both sides of the equation correctly.**

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Would you like further details on this process or have any specific questions?

### Related Questions:
1. What is the correct final value of \(s\) in Vincent's equation?
2. How can combining like terms incorrectly affect the overall solution?
3. What would the solution be if Vincent had distributed the terms incorrectly in Step 1?
4. How would Vincent's error in Step 3 affect his division in Step 4?
5. Why is it important to check each step when solving multi-step equations?

**Tip:** Always double-check your arithmetic operations when solving equations, especially when adding, subtracting, or distributing.

Vincent is trying to solve the equation -4(-3 + s) - 10 = 22. His work is shown below:

Step 1: 12 - 4s - 10 = 22
Step 2: -4s + 2 = 22
Step 3: -4s = 24
Step 4: s = -6

Which of the following statements justifies why Vincent’s solution is incorrect?
A. In Step 1, he did not distribute correctly.
B. In Step 2, he did not combine like terms correctly.
C. In Step 3, he did not add/subtract from both sides of the equation correctly.
D. In Step 4, he did not multiply/divide from both sides of the equation correctly.

Vincent's attempt to solve the equation -4(-3 + s) - 10 = 22 contains an error in Step 3, where he did not subtract correctly from both sides. This solution covers algebraic concepts like the distributive property and solving linear equations.

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