The number z is irrational. Which statement about 3 - z is true? Choices: (A)3 - z is rational. (B)3 - z is irrational. (C)3 - z can be rational or irrational, depending on the value of z.

Identify Number 3: Identify the nature of the number 3. 3 is a rational number because it can be expressed as a fraction (3/1).Consider Number z: Consider the nature of the number z. z is given as an irrational number, which means it cannot be expressed as a fraction of two integers.Analyze Operation 3 - z: Analyze the operation 3 - z. Subtracting an irrational number (z) from a rational number (3) will result in an irrational number. This is because the difference between a rational and an irrational number is always irrational.Check for Exceptions: Check for exceptions. There are no exceptions in this case. Unlike the addition or subtraction of two irrational numbers, which can sometimes result in a rational number, the subtraction of an irrational number from a rational number will always yield an irrational number.

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The number $z$ is irrational. Which statement about $3 - z$ is true? $\newline$ Choices: $\newline$ (A) $3 - z$ is rational. $\newline$ (B) $3 - z$ is irrational. $\newline$ (C) $3 - z$ can be rational or irrational, depending on the value of $z$ .

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Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

Full solution

Q. The number

z

is irrational. Which statement about

3 - z

is true?

\newline

Choices:

\newline

(A)

3 - z

is rational.

\newline

(B)

3 - z

is irrational.

\newline

(C)

3 - z

can be rational or irrational, depending on the value of

z

Identify Number $3$ : Identify the nature of the number $3$ . $3$ is a rational number because it can be expressed as a fraction ( $\frac{3}{1}$ ).
Consider Number $z$ : Consider the nature of the number $z$ . $z$ is given as an irrational number, which means it cannot be expressed as a fraction of two integers.
Analyze Operation $3 - z$ : Analyze the operation $3 - z$ . $\newline$ Subtracting an irrational number ( $z$ ) from a rational number ( $3$ ) will result in an irrational number. This is because the difference between a rational and an irrational number is always irrational.
Check for Exceptions: Check for exceptions. $\newline$ There are no exceptions in this case. Unlike the addition or subtraction of two irrational numbers, which can sometimes result in a rational number, the subtraction of an irrational number from a rational number will always yield an irrational number.