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Chapter 1: Problem 136

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

Short Answer

Expert verified
The main differences between solving a linear inequality and a linear equation include the representation of solutions, methods of solving, and rules of operations, particularly the rule of changing the inequality operator direction when multiplying or dividing by a negative number.

Step by step solution

01

Discuss Equality and Inequality

A linear equation is an equation with two variables that produces a line on a graph, whereas a linear inequality produces a region since it's looking for a range of values, not a specific one.
02

Solving Equations vs. Inequalities

When solving linear equations, you are looking for a specific point where the equation is true. However, for linear inequalities, you are looking for a range of points where the inequality holds true. This involves finding the boundary (where the equation holds) and establishing whether this boundary is included in the solution or not.
03

The Rules of Operations

For both, you can add, subtract, multiply, and divide both sides to simplify the equation or inequality. However, when a linear inequality is multiplied or divided by a negative number, the direction of the inequality symbol changes.
04

Representation of the Solutions

The solutions to linear equations can be represented as points on a line, while the solutions to linear inequalities are represented as regions on a graph, either above or below a line, depending on the inequality sign used.

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Most popular questions from this chapter

At the north campus of a performing arts school, \(10 \%\) of the students are music majors. At the south campus, \(90 \%\) of the students are music majors. The campuses are merged into one east campus. If \(42 \%\) of the 1000 students at the east campus are music majors, how many students did the north and south campuses have before the merger?

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Exercises \(177-179\) will help you prepare for the material covered in the next section. Use the special product \((A+B)^{2}=A^{2}+2 A B+B^{2}\) to multiply: \((\sqrt{x+4}+1)^{2}\)
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