Answer Key for Lesson 7.1 Graphing Inequalities Pages 411-418

If you’re working through problems involving linear inequalities and need a clear breakdown of how to plot solutions, follow these steps. The graphing method is essential for visualizing the range of values that satisfy a given inequality.

Start by identifying the inequality’s boundary. This will typically be the equation of a line, which can be graphed as a solid or dashed line depending on the inequality sign. For example, use a solid line for ≤ or ≥, and a dashed line for . Once the boundary is plotted, determine the shading area by testing a point not on the line–usually the origin (0,0) is a good candidate unless the line passes through it.

To check the region, substitute the coordinates of the test point into the inequality. If the inequality holds true, shade the area that includes this point; if not, shade the opposite side. This will give you a visual representation of all possible solutions that satisfy the condition.

Important Note: Be precise with your shading. Overlapping regions or errors in drawing the boundary line can lead to incorrect results. Always double-check the sign of the inequality and ensure your graphing technique is consistent.

For a deeper understanding of each problem and its solution, review the step-by-step explanations provided for the exercises. This will guide you through the process and help reinforce the concept of graphing solutions to linear inequalities.