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

Identify Number 6: Identify the nature of the number 6. 6 is a whole number, and all whole numbers are rational numbers.Properties of Irrational Numbers: Understand the properties of irrational numbers. An irrational number minus a rational number is always irrational.Apply Property to Problem: Apply the property to the given problem. Since x is irrational and 6 is rational, x - 6 must be irrational.

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

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Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

Full solution

Q. The number

x

is irrational. Which statement about

x - 6

is true?

\newline

Choices:

\newline

(A)

x - 6

is rational.

\newline

(B)

x - 6

is irrational.

\newline

(C)

x - 6

can be rational or irrational, depending on the value of

x

Identify Number $6$ : Identify the nature of the number $6$ . $6$ is a whole number, and all whole numbers are rational numbers.
Properties of Irrational Numbers: Understand the properties of irrational numbers. An irrational number minus a rational number is always irrational.
Apply Property to Problem: Apply the property to the given problem. $\newline$ Since $x$ is irrational and $6$ is rational, $x - 6$ must be irrational.