Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 3 - Section 3.6 - Graphing Linear Inequalities in Two Variables - Exercise Set: 32

Answer

Refer to the image below for the graph.
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Work Step by Step

To graph the given inequality, perform the following steps: (1) Graph the boundary line $y=\frac{2}{5}x-3$ using a dashed line since it involves $\lt$. (refer to the image below for the graph) (2) Use the test point $(0, 0)$. Substitute the x and y values of this point into the given inequality to obtain: \begin{array}{ccc} \\&0&\lt &\frac{2}{5}(0)-3 \\&0 &\lt &0-3 \\&0 &\lt &-3 \end{array} The statement is false. (3) The resulting statement in step (2) is false. This means that the solution set is the region that does not contain the test point $(0, 0)$. To complete the graph, shade the region that does not contain $(0, 0)$. (refer to the attached image in the answer part above for the graph)
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