/*! 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 116 Describe ways in which solving a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 116

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

Short Answer

Expert verified
The three main differences between solving linear inequalities and linear equations are: 1. The use of inequality symbols in inequalities as opposed to an equality symbol in equations. 2. Solution presentation - where inequalities solutions are displayed as ranges, and equations as specific points. 3. Handling multiplication and division by negative numbers, which requires flipping the inequality symbol in inequalities.

Step by step solution

01

Difference 1: Symbols

When solving a linear equation, one looks for an equal balance between both sides of the equation, denoted by the use of the equality symbol \(=\). Conversely, in a linear inequality, one looks for an unequal relationship between both sides, marking this with an inequality symbol such as \(<\), \(>\), \(\leq\), or \(\geq\).
02

Difference 2: Solution Representation

The solution of a linear equation is a specific value or set of values, while the solution of a linear inequality is often a range of values. When representing these solutions, a linear equation's solution is usually represented as a point on a number line or a coordinate on a graph, while a linear inequality's solution is shown as a range or section on a number line or an area on a graph.
03

Difference 3: Handling Multiplication and Division by Negative Numbers

The process of solving both linear equations and inequalities involves manipulating the equations to solve for the desired variable. As part of this manipulation, multiplying or dividing might be necessary. When dealing with a linear equation, multiplying or dividing both sides by a negative number doesn't affect the equation. But in a linear inequality, if you multiply or divide by a negative number, the inequality symbol must be flipped to maintain the relationship between both sides.

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

What are supplementary angles? Describe how to find the measure of an angle's supplement.

According to the American Bureau of Labor Statistics, you will devote 37 years to sleeping and watching TV. The number of years sleeping will exceed the number of years watching TV by 19. Over your lifetime, how many years will you spend on each of these activities?According to the American Bureau of Labor Statistics, you will devote 32 years to sleeping and eating. The number of years sleeping will exceed the number of years eating by 24 Over your lifetime, how many years will you spend on each of these activities?

Solve each equation in using both the addition and multiplication properties of equality. Check proposed solutions. $$-x-3=3$$

Solve each equation in using both the addition and multiplication properties of equality. Check proposed solutions. $$6 z-5=z+5$$

Use the addition property of inequality to solve each inequality and graph the solution set on a number line. \(x-5 \geq 2\)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

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.