/*! 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. 2.148 Solve the below inequality, grap... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Log out

Learning Materials

Features

Discover

Chapter 2: Q. 2.148 (page 204)

Solve the below inequality, graph the solution and write the solution in interval notation:

4x-5≤3

Short Answer

Expert verified

The solution of the inequality is 12≤x≤2.

Interval notation: 12,2

Graph of the inequality is:

Step by step solution

01

Step 1. Given Information.

We have:

4x-5≤3

02

Step 2. Write the equivalent compound inequality.  

4x-5≤3

Apply absolute rule: If |u| ≤ a, a > 0 then -a ≤ u ≤ a

-3≤ 4x-5≤ 3

03

Step 3. Solve the compound inequality.  

Break the compound inequality:

-3≤ 4x-5and  4x-5≤ 3

First, solve -3≤ 4x-5:

Switch sides:

4x-5≥ -34x-5+5≥ -3+54x≥ 24x4≥24x≥12

Now, solve  4x-5≤ 3:

4x-5+5≤ 3+54x≤ 84x4≤84x≤ 2

Merge overlapping intervals:

12≤ x≤ 2

Interval notation:12, 2

04

Step 4. Graph the solution.  

Mark the point 12with a closed circle as it is included in the solution. Mark the point 2with a closed circle as it is included in the solution.

As the solution is attached with "and" the intersection of solution should be done, hence mark all the common points of the solutions:

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 91Ó°ÊÓ!

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

Vina has $4.70in quarters, dimes and nickels in her purse. She has eight more dimes than quarters and six more nickels than quarters. How many of each coin are in her purse?

In the following exercises, use the Pythagorean theorem to find the length of the leg. Round to the nearest tenth if necessary.

Solve the linear equation4p-4-p+7=5p-3.

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?

In the following exercises, find (a) the amount of the mark-up and (b) the list price.

Tom paid $0.60 a pound for tomatoes to sell at his produce store. He added a 33% mark-up. What price did he charge his customers for the tomatoes?`
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

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.