Math  /  Algebra

Question(2) Peyton says the sum of two numbers can never be zero. Explain why Peyton's reasoning is incorrect. Use a model. Show your work.

Studdy Solution

STEP 1

1. We are considering the sum of two real numbers.
2. We need to demonstrate that the sum of two numbers can indeed be zero.

STEP 2

1. Define the concept of additive inverses.
2. Provide a specific example using numbers.
3. Use a model to illustrate the concept.
4. Conclude why Peyton's reasoning is incorrect.

STEP 3

The concept of additive inverses states that for any real number a a , there exists another real number a -a such that their sum is zero.

STEP 4

Consider the number 3 3 . Its additive inverse is 3 -3 . The sum of these two numbers is:
3+(3)=0 3 + (-3) = 0

STEP 5

To model this, imagine a number line. Place a point at +3 +3 and another at 3 -3 . The sum of these points, or their movement towards zero, results in reaching the origin, which represents zero.

STEP 6

Peyton's reasoning is incorrect because the existence of additive inverses allows two numbers to sum to zero. The example of 3 3 and 3 -3 clearly shows that their sum is zero.
The reasoning is incorrect because the sum of a number and its additive inverse is always zero.

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