/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 3 Express each interval in set-bui... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 3

Express each interval in set-builder notation and graph the interval on a number line. $$(-2,4]$$

Short Answer

Expert verified
The interval \(-2,4]\) is represented in set-builder notation as \{x | -2 < x 鈮� 4\}. The graph consists of a number line where -2 is represented by an open circle and 4 is represented by a closed dot, with a line connecting them.

Step by step solution

01

Understanding Interval Notation

The given interval is \(-2,4]\). In interval notation, parentheses '()' imply that the number is not included, whereas brackets '[]' suggest that the number is included.
02

Converting to Set-builder Notation

The formula for converting an interval to set-builder notation is as follows: For an interval (a, b) or [a, b], the set-builder notation will be: \{x | a < x < b\} or \{x | a 鈮� x 鈮� b\}. In the given interval, \(-2\) is not included, meaning it is less than x. Meanwhile, \(4\) is included, meaning x is less than or equals to \(4\). Therefore, using the set builder notation formula, it can be expressed as \{x | -2 < x 鈮� 4\}.
03

Drawing the Interval on a Number Line

On the number line, plot two points representing -2 and 4. Because -2 is not included in the interval, it will be represented by an open circle. 4 is included in the interval and so is represented by a closed dot. Draw a line connecting the two points.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{2 x-1}{x-7}+\frac{3 x-1}{x-7}-\frac{5 x-2}{x-7}=0$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$6+\frac{1}{x}=\frac{7}{x}$$

The rational expression $$\frac{130 x}{100-x}$$ describes the cost, in millions of dollars, to inoculate \(x\) percent of the population against a particular strain of flu. a. Evaluate the expression for \(x=40, x=80,\) and \(x=90\) Describe the meaning of each evaluation in terms of percentage inoculated and cost. b. For what value of \(x\) is the expression undefined? c. What happens to the cost as \(x\) approaches \(100 \% ?\) How can you interpret this observation?

When graphing the solutions of an inequality, what does a parenthesis signify? What does a square bracket signify?

Explain how to simplify a rational expression.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.