Question

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



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 \(x = -1\).