The number x is irrational. Which statement about 2 + x is true? Choices: (A)2 + x is rational. (B)2 + x is irrational. (C)2 + x can be rational or irrational, depending on the value of x.

Identify Number 2: Identify the nature of the number 2. 2 is a rational number because it can be expressed as a fraction of two integers (2/1).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 results in an irrational number. This is because the sum cannot be expressed as a fraction of two integers.Apply Analysis: Apply the analysis to the given problem. Since 2 is rational and x is irrational, the sum 2 + x is irrational.

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The number $x$ is irrational. Which statement about $2 + x$ is true? $\newline$ Choices: $\newline$ (A) $2 + x$ is rational. $\newline$ (B) $2 + x$ is irrational. $\newline$ (C) $2 + x$ can be rational or irrational, depending on the value of $x$ .

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Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

Full solution

Q. The number

x

is irrational. Which statement about

2 + x

is true?

\newline

Choices:

\newline

(A)

2 + x

is rational.

\newline

(B)

2 + x

is irrational.

\newline

(C)

2 + x

can be rational or irrational, depending on the value of

x

Identify Number $2$ : Identify the nature of the number $2$ . $2$ is a rational number because it can be expressed as a fraction of two integers $(2/1)$ .
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 results in an irrational number. This is because the sum cannot be expressed as a fraction of two integers.
Apply Analysis: Apply the analysis to the given problem. $\newline$ Since $2$ is rational and $x$ is irrational, the sum $2 + x$ is irrational.