The number q is irrational. Which statement about q - 4 is true? Choices: (A)q - 4 is rational. (B)q - 4 is irrational. (C)q - 4 can be rational or irrational, depending on the value of q.

Identify Number 4: Identify the nature of the number 4. 4 is a whole number, and any whole number is a rational number.Subtract Rational from Irrational: Consider the subtraction of a rational number from an irrational number. Subtracting a rational number from an irrational number will result in an irrational number. This is because the difference between a rational and an irrational number cannot be expressed as a ratio of two integers.Apply Principle to Problem: Apply this principle to the given problem. Since q is irrational and 4 is rational, q - 4 will also be irrational.

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The number $q$ is irrational. Which statement about $q - 4$ is true? $\newline$ Choices: $\newline$ (A) $q - 4$ is rational. $\newline$ (B) $q - 4$ is irrational. $\newline$ (C) $q - 4$ can be rational or irrational, depending on the value of $q$ .

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Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

Full solution

Q. The number

q

is irrational. Which statement about

q - 4

is true?

\newline

Choices:

\newline

(A)

q - 4

is rational.

\newline

(B)

q - 4

is irrational.

\newline

(C)

q - 4

can be rational or irrational, depending on the value of

q

Identify Number $4$ : Identify the nature of the number $4$ . $4$ is a whole number, and any whole number is a rational number.
Subtract Rational from Irrational: Consider the subtraction of a rational number from an irrational number. Subtracting a rational number from an irrational number will result in an irrational number. This is because the difference between a rational and an irrational number cannot be expressed as a ratio of two integers.
Apply Principle to Problem: Apply this principle to the given problem. $\newline$ Since $q$ is irrational and $4$ is rational, $q - 4$ will also be irrational.