/*! 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. 372 In the following exercises, solv... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Q. 372 (page 977)

In the following exercises, solve each inequality algebraically and write any solution in interval notation.
x2+x-6鈮�0

Short Answer

Expert verified

The solution in interval notation is [-3,2].

Step by step solution

01

Step 1. Given information.

The given inequality is:

x2+x-6鈮�0

02

Step 2. Determine the critical points.

Change the inequality sign to an equal sign and then solve the equation.

x2+x-6=0

Split the middle term.

x2+3x-2x-6=0x(x+3)-2(x+3)=0(x+3)(x-2)=0x=-3,2

The two critical points -3and 2 divide the number line is three intervals (-鈭�,-3),(-3,2),(2,鈭�).

03

Step 3. Determine the intervals where the inequality is correct.

Signs of each of the factors and the sign of the product are shown in the number line.

From the above number line it is clear that (x+3)(x-2)鈮�0over the interval [-3,2].

04

Step 4. Conclusion.

The solution in interval notation is [-3,2].

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 by using the Quadratic Formula:3y(y-2)-3=0

rectangular table for the dining room has a

surface area of 24 square feet. The length is two more feet than twice the width of the table. Find the length and width of the table.

Two painters can paint a room in 2 hours if they work together. The less experienced painter takes 3 hours more than the more experienced painter to finish the job. How long does it take for each painter to paint the room individually?

Explain the procedure for solving an equation in quadratic form.

John has a 10-foot piece of rope that he wants to use to support his 8-foot tree. How far from the base of the tree should he secure the rope?
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Discrete 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.