The number x is irrational. 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 rational number because it can be expressed as a ratio of two integers (10/1).Consider Number Sum: Consider the sum of a rational number and an irrational number. The sum of a rational number and an irrational number is always irrational. This is because if it were rational, then subtracting the rational number from both sides would leave an irrational number equal to a rational number, which is a contradiction.Apply Rule to Numbers: Apply the rule to the given numbers. Since 10 is rational and x is irrational, 10 + x must be irrational.

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The number $x$ is irrational. 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 irrational. 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 rational number because it can be expressed as a ratio of two integers ( $\frac{10}{1}$ ).
Consider Number Sum: Consider the sum of a rational number and an irrational number. The sum of a rational number and an irrational number is always irrational. This is because if it were rational, then subtracting the rational number from both sides would leave an irrational number equal to a rational number, which is a contradiction.
Apply Rule to Numbers: Apply the rule to the given numbers. $\newline$ Since $10$ is rational and $x$ is irrational, $10 + x$ must be irrational.