## Big Ideas Math - Algebra 1, A Common Core Curriculum

Published by Big Ideas Learning LLC

# Chapter 2 - Solving Linear Inequalities - 2.1 - Writing and Graphing Inequalities - Exercises - Page 58: 3

#### Answer

To graph an iequality, make sure that the variable is isolated on one side of the inequality. Then, determine if the inequality involves equality or not so you would know if you will use a close circle or not. Finally, choose a. test number to know which region will be shaded. (Refer to the step-by-step part for complete details,)

#### Work Step by Step

To graph an inequality, perform the following steps: $(1)$ Isolate the variable on one side of the inequality. $(2)$ Determine if the inequality involves equality or not. If the inequality involves an equal sign (e.g., $\leq$ or $\geq$) use a closed circle (or solid dot). Otherwise, use an open circle (or hollow dot). $(3)$ After determining whether a closed or open circle will be used, choose a test number and check whether or not it is a solution of the inequality. If the test number is a solution, shade the region where the test number belongs. Otherwise, shade the region on. the other side. Example: Graph $x+2>5$ $(1)$. Isolate the variable on one side of the inequality: \begin{align*} x+2-2&>5-2\\ x&>3 \end{align*} $(2)$ The inequality does not involve an equal sign so an open circle will be used. $(2)$ Using $5$ as a test number, we'd have: \begin{align*} x+2&>5\\\ 5+2&>5\\ 7&>5 \end{align*} $5$ is a solution of the inequality therefore we shade the region where the test number belongs. Refer to the graph below.

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