/*! 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 103 Write a rational inequality whos... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 103

Write a rational inequality whose solution set is \((-\infty,-4) \cup[3, \infty)\)

Short Answer

Expert verified
The rational inequality whose solution set is \(-\infty,-4) \cup [3, \infty)\ is \( \frac{x+4}{x-3}\geq 0\)

Step by step solution

01

Identify the Critical Points

The critical points from this problem are -4 and 3. They split the number line into the intervals \( (-\infty,-4), (-4,3), and (3, \infty) \). Identify the critical points and understand their importance in formulating the inequality.
02

Formulate the Inequality

Form an inequality where these critical numbers are the roots of a rational function. A sensible option to realise this is: \( \frac{x+4}{x-3}\geq 0 \). For this function, x = -4 and x = 3 are the roots. Next step would be to solve this inequality and compare its solution with the given one.
03

Solve the Inequality

Solve the inequality \( \frac{x+4}{x-3}\geq 0 \). The set solution for this inequality matches the given intervals which are \(-\infty,-4) \cup [3, \infty) \). This confirmed that \( \frac{x+4}{x-3}\geq 0 \) is the correct inequality.

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 each inequality in Exercises \(65-70\) and graph the solution set on a real number line. $$ \left|x^{2}+2 x-36\right|>12 $$

Use long division to rewrite the equation for \(g\) in the form $$\text {quotient }+\frac{\text {remainder}}{\text {divisor}}$$ Then use this form of the function's equation and transformations. $$g(x)=\frac{2 x-9}{x-4}$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. As production level increases, the average cost for a company to produce each unit of its product also increases.

Use the position function $$ s(t)--16 t^{2}+v_{0} t+s_{0} $$ \(\left(v_{11}=\text { initial velocity, } s_{0}-\text { initial position, } t-\text { time }\right)\) to answer Exercises \(75-76\) You throw a ball straight up from a rooftop 160 feet high with an initial velocity of 48 feet per second. During which time period will the ball's height exceed that of the rooftop?

Find the slant asymptote of the graph of each rational function and b. Follow the seven-step strategy and use the slant asymptote to graph each rational function. $$f(x)=\frac{x^{2}+4}{x}$$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Geometry

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.