The number z is irrational. Which statement about 5 - z is true? Choices: (A)5 - z is rational. (B)5 - z is irrational. (C)5 - z can be rational or irrational, depending on the value of z.

Identify Number Type: Identify whether the number 5 is a rational or irrational number. 5 is a whole number, and all whole numbers are rational numbers.Consider Properties: Consider the properties of rational and irrational numbers. The difference between a rational number and an irrational number is always irrational.Apply Property: Apply the property to the given problem. Since 5 is rational and z is irrational, 5 - z must be irrational.

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The number $z$ is irrational. Which statement about $5 - z$ is true? $\newline$ Choices: $\newline$ (A) $5 - z$ is rational. $\newline$ (B) $5 - z$ is irrational. $\newline$ (C) $5 - z$ can be rational or irrational, depending on the value of $z$ .

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Math Problems

Algebra 1

Properties of operations on rational and irrational numbers

Full solution

Q. The number

z

is irrational. Which statement about

5 - z

is true?

\newline

Choices:

\newline

(A)

5 - z

is rational.

\newline

(B)

5 - z

is irrational.

\newline

(C)

5 - z

can be rational or irrational, depending on the value of

z

Identify Number Type: Identify whether the number $5$ is a rational or irrational number. $5$ is a whole number, and all whole numbers are rational numbers.
Consider Properties: Consider the properties of rational and irrational numbers. The difference between a rational number and an irrational number is always irrational.
Apply Property: Apply the property to the given problem. $\newline$ Since $5$ is rational and $z$ is irrational, $5 - z$ must be irrational.