Question

x + (–a) is rational because _______________________.

A. it is the sum of two rational numbers.
B. it is the sum of two irrational numbers.
C. it represents a non-terminating, non-repeating decimal.
D. its terms cannot be combined.

Answer 1

it depends. It can be any constants x and a that rational to get A, or irrational (like square cube or any other sorts for example) to get B.
It can be d if a or x is an imaginary/complex number.

Answer 2

if a or x (but not both are complex it is then D.

See? it can be any of the choices, depending on what course you take.

Answer 3

What do you mean course?

Answer 4

like have you learned about imaginary numbers. and even if you didn't it is still between A and B.

Answer 5

(imaginary number, \(\normalsize\color{blue}{ \rm i }\) which is equivalent to \(\normalsize\color{blue}{ \rm \sqrt{-1} }\) )

Answer 6

I learned about it but I still don't get it. I'm doing some summer school online thing and I'm on complex numbers.

Answer 7

As I see the problem, the only thing I see is what you wrote in the question box. Maybe there is more context to the problem than what I see ?

Answer 8

Do you want me to show you the whole question?

Answer 9

It would be good :)

Answer 10

Let a be a rational number and b be an irrational number.
Assume that a + b = x and that x is rational.
Then b = x – a = x + (–a).
x + (–a) is rational because _______________________.
However, it was stated that b is an irrational number. This is a contradiction.
Therefore, the assumption that x is rational in the equation a + b = x must be incorrect, and x should be an irrational number.
In conclusion, the sum of a rational number and an irrational number is irrational.

Answer 11

\(\normalsize\color{blue}{ \rm a=rational }\)
\(\normalsize\color{blue}{ \rm b=irrational }\)
\(\normalsize\color{blue}{ \rm a+b~~=~~x~~=~~rational }\)

Answer 12

I think D.

Answer 13

Then I'm going to put D and see if that's right.