The number b is irrational. Which statement about 9 + b is true? Choices: (A)9 + b is rational. (B)9 + b is irrational. (C)9 + b can be rational or irrational, depending on the value of b.

Identify Number 9: Identify the nature of the number 9. 9 is a whole number, and all whole numbers are rational.Consider Number b: Consider the nature of the number b. b is given as an irrational number.Analyze Sum: Analyze the sum of a rational number and an irrational number. The sum of a rational number (9) and an irrational number (b) is always irrational. This is because if it were rational, then subtracting the rational part (9) from the sum would leave us with a rational number, which contradicts the fact that b is irrational.Conclude Result: Conclude the nature of 9 + b. Since 9 is rational and b is irrational, their sum 9 + b must be irrational.

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The number $b$ is irrational. Which statement about $9 + b$ is true? $\newline$ Choices: $\newline$ (A) $9 + b$ is rational. $\newline$ (B) $9 + b$ is irrational. $\newline$ (C) $9 + b$ can be rational or irrational, depending on the value of $b$ .

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Math Problems

Algebra 1

Properties of operations on rational and irrational numbers

Full solution

Q. The number

b

is irrational. Which statement about

9 + b

is true?

\newline

Choices:

\newline

(A)

9 + b

is rational.

\newline

(B)

9 + b

is irrational.

\newline

(C)

9 + b

can be rational or irrational, depending on the value of

b

Identify Number $9$ : Identify the nature of the number $9$ . $9$ is a whole number, and all whole numbers are rational.
Consider Number $b$ : Consider the nature of the number $b$ . $b$ is given as an irrational number.
Analyze Sum: Analyze the sum of a rational number and an irrational number. $\newline$ The sum of a rational number $9$ and an irrational number $b$ is always irrational. This is because if it were rational, then subtracting the rational part $9$ from the sum would leave us with a rational number, which contradicts the fact that $b$ is irrational.
Conclude Result: Conclude the nature of $9 + b$ . $\newline$ Since $9$ is rational and $b$ is irrational, their sum $9 + b$ must be irrational.