The number x is rational. Which statement about 10 - x is true? Choices: (A)10 - x is rational. (B)10 - x is irrational. (C)10 - x can be rational or irrational, depending on the value of x.

Identify Number Nature: Identify the nature of the number 10. 10 is a whole number, which is also a rational number because it can be expressed as a fraction 10/1.Properties of Rational Numbers: Understand the properties of rational numbers. A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, where p and q are integers and q is not zero.Analyze Operation Result: Analyze the operation between two rational numbers. When you subtract a rational number from another rational number, the result is always a rational number. This is because the subtraction of two fractions (which represent rational numbers) is another fraction.Apply Property to Problem: Apply the property to the given problem. Since x is rational and 10 is rational, their difference 10 - x will also be a rational number.

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The number $x$ is rational. Which statement about $10 - x$ is true? $\newline$ Choices: $\newline$ (A) $10 - x$ is rational. $\newline$ (B) $10 - x$ is irrational. $\newline$ (C) $10 - x$ 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

10 - x

is true?

\newline

Choices:

\newline

(A)

10 - x

is rational.

\newline

(B)

10 - x

is irrational.

\newline

(C)

10 - x

can be rational or irrational, depending on the value of

x

Identify Number Nature: Identify the nature of the number $10$ . $10$ is a whole number, which is also a rational number because it can be expressed as a fraction $\frac{10}{1}$ .
Properties of Rational Numbers: Understand the properties of rational numbers. A rational number is a number that can be expressed as the quotient or fraction $\frac{p}{q}$ of two integers, where $p$ and $q$ are integers and $q$ is not zero.
Analyze Operation Result: Analyze the operation between two rational numbers. $\newline$ When you subtract a rational number from another rational number, the result is always a rational number. This is because the subtraction of two fractions (which represent rational numbers) is another fraction.
Apply Property to Problem: Apply the property to the given problem. $\newline$ Since $x$ is rational and $10$ is rational, their difference $10 - x$ will also be a rational number.