James was solving -2(7x - 8) = 30 and ended with x = 23/7. Here is his work.

Question

1) Find his mistake and explain why it was a mistake. 2)Tell him how to correct the problem. 3)Make sure you give him the correct final answer.

Answer 1

Let's analyze James's work step by step and identify the mistake.

1. Finding the mistake: James started with the equation: \[ -2(7x - 8) = 30 \] To solve this, he should have distributed \(-2\) to both terms inside the parentheses. The correct distribution would be: \[ -2 \cdot 7x + 2 \cdot 8 = -14x + 16 \] So, the equation should now read: \[ -14x + 16 = 30 \] If he did not distribute correctly, that's where the mistake could have arisen and led to an incorrect solution for \(x\).

2. How to correct the problem: To correct the problem, follow these steps after correctly distributing: \[ -14x + 16 = 30 \] Next, subtract \(16\) from both sides: \[ -14x = 30 - 16 \] Simplifying gives: \[ -14x = 14 \] Now, divide both sides by \(-14\): \[ x = \frac{14}{-14} = -1 \]

3. Correct final answer: The correct final answer is: \[ x = -1 \]

In summary, James's mistake likely came from incorrect distribution of \(-2\), and the correct final answer is \(x = -1\).