Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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 $x$ .

View step-by-step help

View step-by-step help

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.

More problems from Properties of operations on rational and irrational numbers

Question

Simplify. Write your answer as a proper or improper fraction in simplest form.

\newline

\frac{\frac{10}{9}}{\frac{1}{10}} = \frac{\square}{\square}

Posted 1 month ago

Question

a

b

be rational numbers, and let

b

be non-zero. Is

\frac{a}{b}

rational or irrational?

\newline

1

\newline

\newline

\newline

(C) It can be either rational or irrational

Posted 4 months ago

Question

a

be a non-zero rational number and

b

be an irrational number. Is

\frac{a}{b}

rational or irrational? Choose

1

\newline

\newline

\newline

(C) It can be either rational or irrational

Posted 4 months ago

Question

What is the slope of

y=6 x+2

Posted 4 months ago

Question

\frac{1}{5}+4 h=\frac{1}{3}

\newline

What is the value of

h

in the equation?

Posted 2 months ago

Question

\frac{2}{7} x+\frac{11}{7} x=\frac{3}{5}

\newline

Given the equation, what is the value of

13 x

Posted 10 days ago

Question

3 x+4(2-y)=5 x

\newline

2-y=6 x

\newline

Consider the given system of equations. If

(x, y)

is the solution to the system, then what is the value of

\frac{x}{y}

Posted 26 days ago

Question

y

-intercept of the graph of

y=3 x+7

Posted 4 months ago

Question

y=x+4

\newline

\frac{y+3}{4}=7 x^{2}-x+1

\newline

(a, b)

is a solution to the system of equations shown and

a>0

, what is the value of

a

Posted 4 months ago

Question

0

0939

Posted 2 months ago