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

Identify Number 5: Identify the nature of the number 5. 5 is an integer, and all integers are rational numbers because they can be expressed as the ratio of integers (for example, 5 can be written as 5/1).Properties of Rational Numbers: Understand the properties of rational numbers. The set of rational numbers is closed under addition and subtraction. This means that if you add or subtract two rational numbers, the result is also a rational number.Apply Property to x - 5: Apply the property of rational numbers to the expression x - 5. Since x is a rational number and 5 is a rational number, their difference x - 5 must also be a rational number according to the properties of rational numbers.Conclude Expression x - 5: Conclude the nature of the expression x - 5. Therefore, the statement about x - 5 that is true is that x - 5 is rational.

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

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Math Problems

Algebra 1

Properties of operations on rational and irrational numbers

Full solution

Q. The number

x

is rational. Which statement about

x - 5

is true?

\newline

Choices:

\newline

(A)

x - 5

is rational.

\newline

(B)

x - 5

is irrational.

\newline

(C)

x - 5

can be rational or irrational, depending on the value of

x

Identify Number $5$ : Identify the nature of the number $5$ . $5$ is an integer, and all integers are rational numbers because they can be expressed as the ratio of integers (for example, $5$ can be written as $\frac{5}{1}$ ).
Properties of Rational Numbers: Understand the properties of rational numbers. The set of rational numbers is closed under addition and subtraction. This means that if you add or subtract two rational numbers, the result is also a rational number.
Apply Property to $x - 5$ : Apply the property of rational numbers to the expression $x - 5$ . Since $x$ is a rational number and $5$ is a rational number, their difference $x - 5$ must also be a rational number according to the properties of rational numbers.
Conclude Expression $x - 5$ : Conclude the nature of the expression $x - 5$ . Therefore, the statement about $x - 5$ that is true is that $x - 5$ is rational.