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

Identify Number 7: Identify the nature of the number 7. 7 is a rational number because it can be expressed as a fraction of two integers (7/1).Consider Number r: Consider the nature of the number r. r is given as an irrational number, which means it cannot be expressed as a fraction of two integers.Analyze Operation: Analyze the operation between a rational and an irrational number. The difference between a rational number (7) and an irrational number (r) is always irrational. This is because if 7 - r were rational, then adding r to both sides would give 7 = (7 - r) + r, which would imply that r is rational (since both 7 and 7 - r would be rational). This contradicts the given that r is irrational.

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

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Math Problems

Algebra 1

Properties of operations on rational and irrational numbers

Full solution

Q. The number

r

is irrational. Which statement about

7 - r

is true?

\newline

Choices:

\newline

(A)

7 - r

is rational.

\newline

(B)

7 - r

is irrational.

\newline

(C)

7 - r

can be rational or irrational, depending on the value of

r

Identify Number $7$ : Identify the nature of the number $7$ . $7$ is a rational number because it can be expressed as a fraction of two integers ( $\frac{7}{1}$ ).
Consider Number $r$ : Consider the nature of the number $r$ . $r$ is given as an irrational number, which means it cannot be expressed as a fraction of two integers.
Analyze Operation: Analyze the operation between a rational and an irrational number. The difference between a rational number $7$ and an irrational number $r$ is always irrational. This is because if $7 - r$ were rational, then adding $r$ to both sides would give $7 = (7 - r) + r$ , which would imply that $r$ is rational (since both $7$ and $7 - r$ would be rational). This contradicts the given that $r$ is irrational.