/*! 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. 378 In the following exercises, solv... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Q. 378 (page 977)

In the following exercises, solve each inequality algebraically and write any solution in interval notation.
-x2+8x-11<0

Short Answer

Expert verified

The solution in interval notation is (-鈭�,4-5)鈭�(4+5,鈭�).

Step by step solution

01

Step 1. Given information.

The given inequality is:
-x2+8x-11<0

02

Step 2. Determine the critical points.

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

-x2+8x-11=0

Use the quadratic formula to solve the equation.

x=-8卤(8)2-4(-1)(-11)2(-1)鈭�x=-b卤b2-4ac2ax=-8卤20-2x=-8-2卤25-2x=4卤5

The two critical points 4-5and 4+5divide the number line is three intervals (-鈭�,4-5),(4-5,4+5),(4+5,鈭�).

03

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

Test point for the interval (-鈭�,4-5)is x=0.

-(0)2+8(0)-11=-11<0

Test point for the interval (4-5,4+5)is x=3.

-(3)2+8(3)-11=4>0

Test point for the interval (4+5,鈭�)is x=7.

-(7)2+8(7)-11=-4<0

The inequality -x2+8x-11<0is true over the intervals (-鈭�,4-5)and (4+5,鈭�).

04

Step 4. Conclusion.

The solution in interval notation is (-鈭�,4-5)鈭�(4+5,鈭�).

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 quadratic equation25x2-30x+9=36using square root property

A bullet is fired straight up from a BB gun with initial velocity 1120 feet per second at an initial height of 8 feet. Use the formula h=-16t2+vot+8to determine how many seconds it will take for the bullet to hit the ground. (That is, when will h = 0?)

In the following exercises, solve by using the Quadratic Formula.
2x2-x+1=0

The product of two consecutive odd integers is 99. Find the integers.

In the following exercises, solve by using the Quadratic Formula.
(y+4)(y-7)=18
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

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.