/*! 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 51 Solve each inequality and graph ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 51

Solve each inequality and graph the solution on the number line. .7-x \leq 3 x-1

Short Answer

Expert verified
The solution to the inequality \( .7-x \leq 3x-1 \) is \( x \geq .425 \). This is represented on the number line by a filled in circle at \(.425\) with a line extending to the right to signify inclusion of all numbers greater than or equal to \(.425\).

Step by step solution

01

Rewriting the inequality

Rewrite the inequality \( .7 - x \leq 3x - 1 \) to put all x terms on one side and constants on the other. Subtracting \( .7 \) on both sides gives \( -x \leq 3x -1.7 \). Adding \( x \) to both sides gives \( 0 \leq 4x - 1.7 \)
02

Solve for x

Solving the resulting inequality \( 0 \leq 4x - 1.7 \) for \( x \) involves adding \( 1.7 \) on both sides to get \( 1.7 \leq 4x \). Finally, divide both sides by 4 to isolate \( x \), yielding \( x \geq .425 \). Note that the inequality symbol points towards \( x \) indicating that \( x \) is greater than or equal to \(.425\).
03

Graphing the Solution on the Number Line

To graph the solution \( x \geq .425 \) on the number line, mark \(.425\) on the number line and draw a circle around it. Since \( x \geq .425 \) includes \(.425\), fill in the circle to indicate that it is part of the solution. Draw a line extending to the right of \(.425\), indicating that all numbers greater than or equal to \(.425\) are part of the solution.

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. One-seventh of the senior class is living in off-campus housing. If 217 students live off campus, how large is the senior class?

Solve each inequality and graph the solution on the number line. $$-4 \leq-4 x < 12$$

Create a mixture problem of your own, and solve it.

A college professor wants to supplement her retirement income with investment interest. If she invests \(\$ 15,000\) at \(6 \%\) annual interest, how much more would she have to invest at \(7 \%\) to achieve a goal of \(\$ 1,250\) in supplemental income?

Solve each equation and round the result to the nearest tenth. $$\frac{3.7(2.3 x-2.7)}{1.5}=5.2(x-1.2)$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

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.