To answer this question, we have that if we sum two rational numbers, the number will be also a rational number.
In the proof, we have that in Step 5, we are adding algebraically two rational numbers. The result will be also a rational number.
Therefore, we have:
Which of the following best completes the proof?
It is the sum of two rational numbers.
It is that way because the sum of two rational numbers is also a rational number. We know that a rational number can be expressed as a fraction of integers, one of them in the numerator, and the other in the denominator. Therefore, if we algebraically add two rational numbers, we will get a rational number too.
In summary, we have that (in Step 5):
x + (-a) is a rational number because it is the sum of two rational numbers (first option).
[A non-terminating, non-repeating decimal is an irrational number, like π (3.1415926535...) or Euler's number (e = 2.7182818284...), or the square root of 2 (1.4142135623...).]