/*! 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 1: Problem 3

Express each interval in set-builder notation and graph the interval on a number line. $$[-5,2)$$

Short Answer

Expert verified
The interval \([-5,2)\] in set-builder notation is \(\{x | -5 \leq x < 2\}\). In the number line graph, -5 is represented by a filled circle and 2 by an open circle, with a line connecting the two.

Step by step solution

01

Expressing in Set-Builder Notation

In set-builder notation, the interval \([-5,2)\] can be represented as \(\{x | -5 \leq x < 2\}\). This denotes the set of all x such that x is greater than or equal to -5 and less than 2.
02

Graphing on a Number Line

On the number line, locate -5 and 2. Draw a solid circle at -5 to show that -5 is included in the interval. Draw an open circle at 2 to represent that 2 is not included in the interval. Draw a line to connect these two circles, representing all the numbers lying in between.
03

Considering the direction of inequality

The \( \leq \) symbol in the \( -5 \leq x \) indicates that the point at \( -5 \) should be filled, while \( < \) in \( x < 2 \) indicates the point at \( 2 \) should be an open circle to show 2 is not included.

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

In Exercises \(115-122,\) find all values of \(x\) satisfying the given conditions. $$ y_{1}=\frac{2 x}{x+2}, y_{2}=\frac{3}{x+4}, \text { and } y_{1}+y_{2}=1 $$

Exercises \(177-179\) will help you prepare for the material covered in the next section. Factor completely: \(x^{3}+x^{2}-4 x-4\)

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? $$V=\pi r^{2} h \text { for } h$$

The price of a dress is reduced by \(40 \% .\) When the dress still does not sell, it is reduced by \(40 \%\) of the reduced price. If the price of the dress after both reductions is \(\$ 72,\) what was the original price?

In Exercises \(127-130,\) solve each equation by the method of your choice. $$ \frac{x-1}{x-2}+\frac{x}{x-3}=\frac{1}{x^{2}-5 x+6} $$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Applied Mathematics

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.