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Chapter 1: Problem 3

Consider the subtraction \(5-(-7)\) a. Find the opposite, or additive inverse, of \(-7\) b. Rewrite the subtraction as the addition of the opposite of \(-7\)

Short Answer

Expert verified
The additive inverse of -7 is 7, and the subtraction 5-(-7) can be rewritten as the addition problem 5 + 7, which equals 12.

Step by step solution

01

Find the additive inverse of -7

An additive inverse, or opposite, is a number that when added to the original number gives a sum of 0. Since 7 + (-7) = 0, 7 is the additive inverse, or opposite, of -7.
02

Rewrite the subtraction as the addition of the opposite

Having identified the additive inverse of -7 as 7, the given subtraction problem, 5 - (-7), can be rewritten as 5 + 7, replacing the -(-7) (subtracting negative 7) with +7, which is essentially adding positive 7.
03

Evaluate the expression

To obtain the final answer, perform the addition 5 + 7 which sums up to 12.

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