/*! 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 55 Solve each compound inequality. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 55

Solve each compound inequality. $$-3 \leq \frac{2}{3} x-5<-1$$

Short Answer

Expert verified
The solution to the compound inequality \(-3 \leq \frac{2}{3}x-5<-1\) is \(3 \leq x < 6\)

Step by step solution

01

Isolate the Expression

The first step is to isolate the expression \(\frac{2}{3}x-5\) in the center of both inequalities. This can be done by adding 5 to all parts of the inequality: \n\n\(-3+5 \leq \frac{2}{3}x-5+5 < -1+5\)\n\nThis simplifies to: \n\n\(2 \leq \frac{2}{3}x < 4\)
02

Isolate the Variable

Now, the next step is to isolate \(x\) by multiplying all parts of the inequality by the reciprocal of \(\frac{2}{3}\), which is \(\frac{3}{2}\).\n\n Hence, we have,\n\n\(2 * \frac{3}{2} \leq \frac{2}{3}x * \frac{3}{2} < 4 * \frac{3}{2}\)\n\n Simplifying this gives: \n\n \(3 \leq x < 6\)
03

Interpret the Solution

The solution \(3 \leq x < 6\) means that any number \(x\) that is greater than or equal to 3 and less than 6 is a solution to the original compound 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

Exercises \(142-144\) will help you prepare for the material covered in the next section. Use the distributive property to multiply: $$ 2 x^{4}\left(8 x^{4}+3 x\right) $$

The average rate on a round-trip commute having a one-way distance \(d\) is given by the complex rational expression $$\frac{2 d}{\frac{d}{r_{1}}+\frac{d}{r_{2}}}$$ in which \(r_{1}\) and \(r_{2}\) are the average rates on the outgoing and return trips, respectively. Simplify the expression. Then find your average rate if you drive to campus averaging 40 miles per hour and return home on the same route averaging 30 miles per hour. Explain why the answer is not 35 miles per hour.

Describe ways in which solving a linear inequality is different than solving a linear equation.

Will help you prepare for the material covered in the next section. If the width of a rectangle is represented by \(x\) and the length is represented by \(x+200\), write a simplified algebraic expression that models the rectangle's perimeter.

Describe two ways to simplify \(\frac{\frac{3}{x}+\frac{2}{x^{2}}}{\frac{1}{x^{2}}+\frac{2}{x}}\).
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

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.