/*! 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} Q. 427 Gregory is thinking of a number ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q. 427 (page 196)

Gregory is thinking of a number and he wants his sister Lauren to guess the number. His first clue is that the six less than twice his number is between four and forty-two. Write the compound inequality that shows the range of numbers that Gregory might be thinking of.

Short Answer

Expert verified

The compound inequality is 5鈮�n鈮�24and the range is5,24.

Step by step solution

01

Step 1. Given information.

We have:

Gregory wants his sister Lauren to guess the number. His first clue is that the six less than twice his number is between four and forty-two.

02

Step 2. Find the compound inequality. 

Let the number ben.

6less than twice the number ncan be modeled as:

2n-6

As the number 2n-6lies between 4and 42, it follows that:

4鈮�2n-6

2n-6鈮�42

Write the compound inequality as:

4鈮�2n-6鈮�42

03

Step 3. Solve the compound inequality. 

We have:

4鈮�2n-6鈮�42

Break the inequality as 4鈮�2n-6and role="math" localid="1644902645745" 2n-6鈮�42. First, solve 4鈮�2n-6Switch sides:

2n-6鈮�鈥�42n-6+6鈮�鈥�4+62n鈮�鈥�102n2鈮�102n鈮�鈥�5

Now, solve2n-6鈮�42:

Add 6to both sides:

2n-6+6鈮�鈥�42+62n鈮�鈥�482n2鈮�482n鈮�鈥�24

By combining both solution, we get the range:

5鈮�鈥�n鈮�鈥�24

Interval notation:5,鈥�24

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

Solve the linear equation92m-3-8=4m+7.

In the following exercises, find (a) the amount of discount and (b) the sale price.

Errol bought a skateboard helmet on sale at 40% off. The original price was $49.95.

Matt and Chris leave their uncle's house in Phoenix at the same time. Matt drives west on I-60at a speed of 76miles per hour. Chris drives east on I-60at a speed of 82 miles per hour. How many hours will it take them to be 632 miles apart?

The length of the rectangle is three meters less than twice the width. The perimeter of a rectangle is 36 meters. Find the dimensions of the rectangle.

The length of a rectangle is eight feet more than the width. The perimeter is 60 feet. Find the length and width.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

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.