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

Identify Number 5: Identify the nature of the number 5. 5 is a rational number because it can be expressed as a fraction (5/1).Understand Number x: Understand the nature of the number x. x is given as an irrational number, which means it cannot be expressed as a fraction of two integers.Analyze Sum: Analyze the sum of a rational number and an irrational number. Adding a rational number to an irrational number will result in an irrational number. This is because the sum cannot be expressed as a fraction of two integers.Apply Rule: Apply this rule to the given numbers. Since 5 is rational and x is irrational, their sum 5 + x will also be irrational.

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The number $x$ is irrational. Which statement about $5 + x$ is true? $\newline$ Choices: $\newline$ (A) $5 + x$ is rational. $\newline$ (B) $5 + x$ is irrational. $\newline$ (C) $5 + x$ 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 irrational. Which statement about

5 + x

is true?

\newline

Choices:

\newline

(A)

5 + x

is rational.

\newline

(B)

5 + x

is irrational.

\newline

(C)

5 + x

can be rational or irrational, depending on the value of

x

Identify Number $5$ : Identify the nature of the number $5$ . $5$ is a rational number because it can be expressed as a fraction ( $\frac{5}{1}$ ).
Understand Number $x$ : Understand the nature of the number $x$ . $x$ is given as an irrational number, which means it cannot be expressed as a fraction of two integers.
Analyze Sum: Analyze the sum of a rational number and an irrational number. $\newline$ Adding a rational number to an irrational number will result in an irrational number. This is because the sum cannot be expressed as a fraction of two integers.
Apply Rule: Apply this rule to the given numbers. $\newline$ Since $5$ is rational and $x$ is irrational, their sum $5 + x$ will also be irrational.