Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 3 - Solving Inequalities - 3-6 Compound Inequalities - Practice and Problem-Solving Exercises - Page 204: 25

Answer

$x\leq-1$ or $x\gt3$
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Work Step by Step

The "or" tells us this is a compound inequality, so there will be 2 expressions. For the first expression, the infinity on the left tells us that the graph will point to the left with no endpoint, which is a less than operation since numbers on the number line are smaller to the left. The other endpoint is -1. The square bracket tells us that -1 is included in the solution set, so the operation is less than or equal to, and the endpoint on the graph is a solid circle. For the second expression, the infinity on the right tells us that the graph will point to the right with no endpoint, which is a greater than operation since numbers on the number line are larger to the right. The other endpoint is 3. The parenthesis tells us that 3 is not included in the solution set, so the operation is greater than, and the endpoint on the graph is an open circle.
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