Question

laura determined the difference between 8 and -2 using the additive inverse. her steps are shown below.
8 - (-2) = -8 + 2 = -6
which best describes the error in lauras work?
○ the 8 should have remained positive.
○ the 2 should have remained negative.
○ the addition of -8 and 2 was computed incorrectly.
○ the 8 should have remained positive, and the 2 should have remained negative.

Explanation:

To solve this, we recall the rule for subtracting a negative number: \(a - (-b)=a + b\) (using additive inverse, the additive inverse of \(-2\) is \(2\), so \(8-(-2)=8 + 2\)).

Laura's step: \(8-(-2)=-8 + 2\) is wrong. The error is that the \(8\) was incorrectly made negative; it should have remained positive. Let's analyze each option:

• Option 1: "The 8 should have remained positive." This matches the error (since \(8-(-2)\) should be \(8 + 2\), not \(-8+2\)).
• Option 2: The \(2\) comes from the additive inverse of \(-2\), so it should be positive, so this is wrong.
• Option 3: The addition of \(-8\) and \(2\) is \(-6\), but the main error is the sign of \(8\), not the addition of \(-8\) and \(2\) (since the initial transformation was wrong).
• Option 4: The \(2\) should be positive (additive inverse of \(-2\) is \(2\)), so this is wrong.

Answer:

A. The 8 should have remained positive.