## Elementary Algebra

Published by Cengage Learning

# Chapter 8 - Coordinate Geometry and Linear Systems - 8.7 - Graphing Linear Inequalities - Problem Set 8.7 - Page 384: 21

#### Answer

To graph an inequality, we first pretend that the inequality sign is an equal sign, and then we graph the equation. If it is a less than or equal to sign or a greater than or equal to sign, we make the line solid. If not, we make the line dashed. Next, we must shade the region. In order to do this, we pick any point not on the line. If that point satisfies the inequality, we shade the region to the side of the line that the point is in. If the point does not satisfy the inequality, we shade the region on the other side of the line. Once we graph one inequality, we can graph the other inequality doing the same thing. The overlap (the purple area on the attached graph) represents the solution to the system of inequalities.

#### Work Step by Step

To graph an inequality, we first pretend that the inequality sign is an equal sign, and then we graph the equation. If it is a less than or equal to sign or a greater than or equal to sign, we make the line solid. If not, we make the line dashed. Next, we must shade the region. In order to do this, we pick any point not on the line. If that point satisfies the inequality, we shade the region to the side of the line that the point is in. If the point does not satisfy the inequality, we shade the region on the other side of the line. Once we graph one inequality, we can graph the other inequality doing the same thing. The overlap (the purple area on the attached graph) represents the solution to the system of inequalities.

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