Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 3 - Solving Inequalities - 3-6 Compound Inequalities - Practice and Problem-Solving Exercises: 54

Answer

F

Work Step by Step

If a student must earn at least 24 credits, then the student's credits must be greater than or equal to 24. Let c be the number of credits. F says credits must be less than or equal to 24, which is not correct. If the student only had 23 credits, he would not be able to graduate. G states that credits must be greater than or equal to 24, which correctly describes the situation. H says 24 must be less than or equal to the number of credits, which is another way of saying that credits must be greater than or equal to 24. 24≤c⟶ subtract c and subtract 24 from each side 24−c−24≤c−c−24⟶ subtract −c≤−24⟶ multiply each side by -1; reverse the inequality sign −c×−1≥−24×−1⟶ multiply c≥24 I also correctly describes the situation. The graph indicates that c is greater than or equal to 24 because the arrow extends to the right, in the direction of increasing values. 24 is shown as included in the solution set by the solid circle at the endpoint.
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