Austin worked out the problem to the left and got an answer of

To determine why Lisa might be correct, we'd need to understand the specific problem that Austin and Lisa worked on. Since you mentioned that there is a problem to the left but didn't provide the details, it is impossible for me to analyze or compare their answers without that context.

If you could share the details of the problem Austin worked on, along with both answers he and Lisa arrived at, I would be happy to explain why Lisa might think Austin made a mistake and clarify the reasoning behind it. Please provide that information, and I'll assist you further!

5x-3(x-2)=8
5x-3x-6=8
2x-6=8
2x=14
x=7

Austin worked out the problem to the left and got an answer of


Lisa thinks he made a mistake and the answer should be


Who is correct or are they both wrong? Why?


Explain your thinking of why Lisa is right

Let's go through the steps of Austin's work to see where he might have made a mistake:

1. Start with the original equation: \[ 5x - 3(x - 2) = 8 \]

2. Distribute the \(-3\) through the parentheses: \[ 5x - 3x + 6 = 8 \]

3. Combine like terms: \[ (5x - 3x) + 6 = 8 \] This simplifies to: \[ 2x + 6 = 8 \]

4. Next, subtract \(6\) from both sides: \[ 2x = 8 - 6 \] Which simplifies to: \[ 2x = 2 \]

5. Finally, divide both sides by \(2\): \[ x = 1 \]

So, Austin's final answer of \(x = 7\) is incorrect. The correct solution is \(x = 1\).

Because Lisa thinks he made a mistake, she is correct in this situation. The mistake occurred in the step where Austin combined the terms after the distribution. Instead of correctly combining to \(2x + 6 = 8\), it seems he miscalculated the addition and arrived at an incorrect result.

In conclusion, Austin is wrong, and Lisa is right because the correct solution to the equation is \(x = 1\).