Let's go through the steps of the solution in the box to identify where the student's first error occurs.

Given Equation:

$6 - 2(x + 7) = 10$

Step 1:

$6 - 2x + 14 = 10$ Here, the student distributes $-2$ to both $x$ and $7$, but this is incorrect. The correct distribution should be: $6 - 2x - 14 = 10$ Thus, the error occurs in Step 1, where the student mistakenly added $14$ instead of subtracting $14$.

Correct next steps after fixing Step 1:

1. The correct equation after distribution would be: $6 - 2x - 14 = 10$ Simplifying the constants: $-2x - 8 = 10$
2. Add 8 to both sides: $-2x = 18$
3. Divide both sides by $-2$: $x = -9$

Therefore, the first error occurs in Step 1, and the correct answer is A).

Would you like further details on how I identified the error or solved the correct version?

Follow-up Questions:

1. What is the correct process for distributing negative numbers across parentheses?
2. How do you combine like terms after distribution?
3. Why is dividing by a negative important when solving linear equations?
4. What are the next steps after identifying an error in an algebraic solution?
5. Can you explain how to verify your final solution in an equation?

Tip:

Always carefully check the distribution of negative signs, as they are a common source of errors when solving equations.