Nathan made a mistake in step 3. He divided -24 by 8 to get -3, but the correct answer is 3. He should have divided by -8 instead.
Nathan made a mistake in step 3 of his work.
He incorrectly divided -24 by 8 to get -3.
The correct answer is 3, and he should have divided by -8 instead.
Here's a more detailed explanation of the steps Nathan took and where he went wrong:
Step 1: Nathan correctly multiplied both terms in the parentheses by 3.
Step 2: Nathan incorrectly combined the terms on the left side of the equation. Instead of -2x, he should have written 5x - 3x, which simplifies to 2x.
Step 3 (mistake): Nathan divided -24 by 8 to get -3.
This is incorrect because he divided by a positive number instead of a negative number.
Dividing by -8 would have given him the correct answer of 3.
Step 4: Nathan incorrectly simplified the equation by dividing both sides by 8.
He should have divided by -3 to get x by itself.
Therefore, Nathan's mistake was in step 3 where he divided by the wrong number.
If he had divided by -8 instead, he would have reached the correct answer of x = 3.