The number w is irrational. Which statement about 9 - w is true? Choices: (A)9 - w is rational. (B)9 - w is irrational. (C)9 - w can be rational or irrational, depending on the value of w.

Identify Number 9: Identify the nature of the number 9. 9 is a rational number because it can be expressed as a fraction (9/1).Consider Number w: Consider the nature of the number w. w is given as an irrational number, which means it cannot be expressed as a fraction of two integers.Analyze Operation: Analyze the operation between 9 and w. Subtracting an irrational number w from a rational number 9 will result in an irrational number. This is because the difference between a rational and an irrational number is always irrational.Determine Truth: Determine the truth of the given statements based on the previous analysis. Since 9 - w is the difference between a rational and an irrational number, the result is irrational. Therefore, the correct statement is: (B) 9 - w is irrational.

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The number $w$ is irrational. Which statement about $9 - w$ is true? $\newline$ Choices: $\newline$ (A) $9 - w$ is rational. $\newline$ (B) $9 - w$ is irrational. $\newline$ (C) $9 - w$ can be rational or irrational, depending on the value of $w$ .

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Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

Full solution

Q. The number

w

is irrational. Which statement about

9 - w

is true?

\newline

Choices:

\newline

(A)

9 - w

is rational.

\newline

(B)

9 - w

is irrational.

\newline

(C)

9 - w

can be rational or irrational, depending on the value of

w

Identify Number $9$ : Identify the nature of the number $9$ . $9$ is a rational number because it can be expressed as a fraction ( $\frac{9}{1}$ ).
Consider Number $w$ : Consider the nature of the number $w$ . $w$ is given as an irrational number, which means it cannot be expressed as a fraction of two integers.
Analyze Operation: Analyze the operation between $9$ and $w$ . $\newline$ Subtracting an irrational number $w$ from a rational number $9$ will result in an irrational number. This is because the difference between a rational and an irrational number is always irrational.
Determine Truth: Determine the truth of the given statements based on the previous analysis. $\newline$ Since $9 - w$ is the difference between a rational and an irrational number, the result is irrational. Therefore, the correct statement is: $\newline$ (B) $9 - w$ is irrational.