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The number $y$ is irrational. Which statement about $7 - y$ is true? $\newline$ Choices: $\newline$ (A) $7 - y$ is rational. $\newline$ (B) $7 - y$ is irrational. $\newline$ (C) $7 - y$ can be rational or irrational, depending on the value of $y$ .

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Properties of operations on rational and irrational numbers

Full solution

Q. The number

y

is irrational. Which statement about

7 - y

is true?

\newline

Choices:

\newline

(A)

7 - y

is rational.

\newline

(B)

7 - y

is irrational.

\newline

(C)

7 - y

can be rational or irrational, depending on the value of

y

.

Identify Number Type: Identify whether the number $7$ is a rational or irrational number. $7$ is a whole number and can be expressed as a fraction $\frac{7}{1}$ , so it is a rational number.
Properties of Numbers: Consider the properties of rational and irrational numbers. The difference between a rational number and an irrational number is always irrational. This is because if $7 - y$ were rational, then adding $y$ to both sides would result in $7$ being the sum of a rational and an irrational number, which is not possible.
Analyze Given Choices: Analyze the given choices in the context of the properties of rational and irrational numbers. $\newline$ Since $7$ is rational and $y$ is irrational, their difference $7 - y$ must be irrational.

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