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The following are reasons why 3 and -3 are additive inverses. Check all of the conditions you included in your response.

A) The numbers are opposites of each other.
B) The numbers are the same distance from zero but in different directions.
C) 3 + (-3) = 0

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Final answer:

A) 3 and -3 are additive inverses because they are opposites of each other (A), are equidistant from zero on the number line but in opposite directions (B), and their sum is zero (C), which fulfills the definition of additive inverses.

Step-by-step explanation:

The question is addressing the concept of additive inverses in mathematics, specifically why the numbers 3 and -3 are considered to be additive inverses of each other. The conditions under consideration for these numbers to be additive inverses are: A) The numbers are opposites of each other, B) The numbers are the same distance from zero but in different directions, and C) 3 + (-3) = 0.

To determine why 3 and -3 are additive inverses, let's analyze each condition:

  • A) The numbers 3 and -3 are indeed opposites of each other, which means they are located at the same distance from zero on the number line but on opposite sides.
  • B) This statement is true; the absolute value of both 3 and -3 is 3, indicating they are an equal distance from zero in opposite directions.
  • C) When we add 3 and -3 (3 + (-3)), the sum is zero. This is the defining property of additive inverses; the sum of a number and its additive inverse is always zero.

Therefore, all three conditions A, B, and C correctly describe why 3 and -3 are additive inverses.

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