/*! 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 98 Describe ways in which solving a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 98

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

Short Answer

Expert verified
The key differences between solving linear inequalities and linear equations are that linear inequalities result in range solutions compared to the single solution for an equation, the direction of the inequality sign changes when multiplied or divided by a negative number unlike an equality sign in equations, and the solutions to inequalities when graphed result in a shaded area representing the range of possible solutions whereas the graph of a linear equation is a straight line.

Step by step solution

01

Understanding the nature of solutions

Linear equations result in a single unique solution. Linear inequalities, on the other hand, express a range of solutions. Inequalities can have an infinite number of possible solutions since they don't specify one exact value, but rather a range.
02

Appreciating the role of inequality signs

Unlike in equations, direction of the inequality sign matters a lot in inequalities. When you multiply or divide an inequality by a negative number, the direction of the inequality sign changes (i.e., \'>\' becomes \'<\' or vice versa). This rule doesn't apply in equations.
03

Exploring the graphical representation

When the solutions to both linear equations and inequalities are graphed on a number line or a coordinate plane, the difference becomes very clear. Linear equations have a straight line solution, but linear inequalities give rise to a shaded area or interval, showing the range of potential solutions.

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

In Exercises 73-80, solve each equation by the method of your choice. \(\frac{3 x^{2}}{4}-\frac{5 x}{2}-2=0\)

Use FOIL to find the products. \((2 x-1)(x+2)\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(3 x^{2}-2 x-5\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I began the solution of \(5-3(x+2)>10 x\) by simplifying the left side, obtaining \(2 x+4>10 x\).

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(6 x^{2}-11 x+4\)
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

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.