The number w is irrational. Which statement about 6 - w is true? Choices: (A)6 - w is rational. (B)6 - w is irrational. (C)6 - w can be rational or irrational, depending on the value of w.

Identify Number 6: Identify the nature of the number 6. 6 is a rational number because it can be expressed as a fraction of two integers (6/1).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 Subtraction: Analyze the subtraction of an irrational number from a rational number. The difference between a rational number and an irrational number is always irrational. This is because if 6 - w were rational, then adding w to both sides would imply that 6 is equal to a rational plus an irrational number, which would make 6 irrational. This is a contradiction because we know 6 is rational.Conclude Result: Conclude the nature of 6 - w. Since 6 is rational and w is irrational, their difference 6 - w must be irrational.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The number $w$ is irrational. Which statement about $6 - w$ is true? $\newline$ Choices: $\newline$ (A) $6 - w$ is rational. $\newline$ (B) $6 - w$ is irrational. $\newline$ (C) $6 - w$ can be rational or irrational, depending on the value of $w$ .

View step-by-step help

Home

Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

Full solution

Q. The number

w

is irrational. Which statement about

6 - w

is true?

\newline

Choices:

\newline

(A)

6 - w

is rational.

\newline

(B)

6 - w

is irrational.

\newline

(C)

6 - w

can be rational or irrational, depending on the value of

w

Identify Number $6$ : Identify the nature of the number $6$ . $6$ is a rational number because it can be expressed as a fraction of two integers ( $\frac{6}{1}$ ).
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 Subtraction: Analyze the subtraction of an irrational number from a rational number. The difference between a rational number and an irrational number is always irrational. This is because if $6 - w$ were rational, then adding $w$ to both sides would imply that $6$ is equal to a rational plus an irrational number, which would make $6$ irrational. This is a contradiction because we know $6$ is rational.
Conclude Result: Conclude the nature of $6 - w$ . Since $6$ is rational and $w$ is irrational, their difference $6 - w$ must be irrational.