/*! 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 13 When do you use parentheses when... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 13

When do you use parentheses when writing a solution set in interval notation?

Short Answer

Expert verified
Use parentheses in interval notation when an endpoint is not included in the interval, representing an open interval. For example, for an interval where x is greater than 2 and less than 8, use (2, 8). Use brackets for closed intervals, when an endpoint is included, and use a combination of parentheses and brackets for mixed intervals.

Step by step solution

01

Understand Interval Notation

Interval notation is a method to represent the range of values between two endpoints, for example, x values between a and b. The notation for an interval includes either parentheses or brackets, with the left symbol representing the lower bound and the right symbol representing the upper bound. The parentheses are used when the endpoint is not included in the interval, while brackets are used when the endpoint is included.
02

Open Intervals: Parentheses

Open intervals are intervals that exclude one or both endpoints, which means the values of the endpoints are not part of the interval. Parentheses are used to represent open intervals. If an endpoint is not included in the interval, a parenthesis is used for that endpoint. For example, if we have an interval where x is greater than 2 and less than 8, it would be represented as (2, 8) using parentheses, since the values 2 and 8 are not included in the interval.
03

Closed Intervals: Brackets

Closed intervals are intervals that include one or both endpoints, which means the values of the endpoints are part of the interval. Brackets are used to represent closed intervals. If an endpoint is included in the interval, a bracket is used for that endpoint. For example, if we have an interval where x is greater than or equal to 2 and less than or equal to 8, it would be represented as [2, 8] using brackets, since the values 2 and 8 are included in the interval.
04

Mixed Intervals: Parentheses and Brackets

Sometimes, an interval might include one endpoint and exclude the other. In this case, we use both parentheses and brackets. For example, if we have an interval where x is greater than 2 and less than or equal to 8, it would be represented as (2, 8] using parentheses for the excluded value and a bracket for the included value. In summary, use parentheses when an endpoint is not included in the interval and use brackets when an endpoint is included in the interval.

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

A book is open to two pages numbered consecutively. The sum of the page numbers is \(373 .\) What are the page numbers?

Seven more than twice a number is thirty-five. Find the number. Five more than twice a number is fifty-three. Find the number.

Objectives 2 and 3 Mixed Exercises Solve using the five "Steps for Solving Applied Problems." Tamara invests some money in three different accounts. She puts some of it in a CD earning \(3 \%\) simple interest and twice as much in an IRA paying \(4 \%\) simple interest. She also decides to invest \(\$ 1000\) more than what she's invested in the CD into a mutual fund earning \(5 \%\) simple interest. Determine how much money Tamara invested in each account if she earned \(\$ 290\) in interest after 1 year.

Write an equation and solve. Use the five "Steps for Solving Word Problems." One-sixth of the smallest of three consecutive even integers is three less than one-tenth the sum of the other even integers. Find the integers.

The three top-selling albums of 2002 were by Eminem, Nelly, and Avril Lavigne. Nelly sold 0.8 million more albums than Avril Lavigne while Eminem's album sold 3.5 million more than Avril's. Find the number of albums sold by each artist if together they eold 16.6 million copies.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

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.