/*! 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 65 Solve each inequality and graph ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 65

Solve each inequality and graph the solution set on a number line. \(-3 \leq \frac{2}{3} x-5<-1\)

Short Answer

Expert verified
The solution to the inequality is \( 3 \leq x < 6 \). In the number line, this solution will be represented by a line stretching from a filled dot at 3 to an open circle just before 6.

Step by step solution

01

Isolate the variable x

First, the goal should be to isolate x (the variable). The number 5 is being subtracted from \( \frac{2}{3} \)x, so adding 5 to all sides will help isolate x. This results in \( -3+5 \leq \frac{2}{3} x <-1+5 \), which simplifies to \( 2 \leq \frac{2}{3} x < 4 \). To isolate x further, multiply each side of the inequalities by \( \frac{3}{2} \), resulting in \( 2*\frac{3}{2} \leq x < 4*\frac{3}{2} \), which simplifies to \( 3 \leq x < 6 \).
02

Graph the solution set on a number line

Draw a number line to graph x values that meet both conditions (3 鈮� x and x < 6). For the first condition, include 3 which is shown as a filled dot or closed circle. For the second condition, from 3 to just before 6, draw the line and at 6, draw an open circle representing x is less than but not equal to 6.

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 the equations using the quadratic formula. \(x^{2}+6 x-10=0\)

Solve the quadratic equations by factoring. \(5 x^{2}+x=18\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(3 x^{2}-x-2\)

Solve the equations using the quadratic formula. \(x^{2}+5 x+3=0\)

Solve each equation by the method of your choice. \((2 x-6)(x+2)=5(x-1)-12\)
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

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.