The number x is rational. Which statement about x + 4 is true? Choices: (A)x + 4 is rational. (B)x + 4 is irrational. (C)x + 4 can be rational or irrational, depending on the value of x.

Identify Number 4: Identify the nature of the number 4. 4 is an integer, and all integers are rational numbers because they can be expressed as a ratio of integers (for example, 4 can be written as 4/1).Properties of Rational Numbers: Understand the properties of rational numbers. The sum of two rational numbers is always a rational number. This is because if you have two rational numbers, a/b and c/d, their sum (a/b) + (c/d) can be expressed as a common fraction (ad + bc) / (bd), which is still a ratio of two integers.Apply Property to Problem: Apply the property to the given problem. Since x is a rational number and 4 is a rational number, their sum x + 4 must also be a rational number according to the property of rational numbers.

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The number $x$ is rational. Which statement about $x + 4$ is true? $\newline$ Choices: $\newline$ (A) $x + 4$ is rational. $\newline$ (B) $x + 4$ is irrational. $\newline$ (C) $x + 4$ 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

x + 4

is true?

\newline

Choices:

\newline

(A)

x + 4

is rational.

\newline

(B)

x + 4

is irrational.

\newline

(C)

x + 4

can be rational or irrational, depending on the value of

x

Identify Number $4$ : Identify the nature of the number $4$ . $4$ is an integer, and all integers are rational numbers because they can be expressed as a ratio of integers (for example, $4$ can be written as $\frac{4}{1}$ ).
Properties of Rational Numbers: Understand the properties of rational numbers. The sum of two rational numbers is always a rational number. This is because if you have two rational numbers, $\frac{a}{b}$ and $\frac{c}{d}$ , their sum $\left(\frac{a}{b}\right) + \left(\frac{c}{d}\right)$ can be expressed as a common fraction $\frac{ad + bc}{bd}$ , which is still a ratio of two integers.
Apply Property to Problem: Apply the property to the given problem. $\newline$ Since $x$ is a rational number and $4$ is a rational number, their sum $x + 4$ must also be a rational number according to the property of rational numbers.