Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - 1.1 Real Numbers, Functions, and Graphs - Exercises: 25

Answer

(-3,1)

Work Step by Step

1.) Solve the inequality equation for 0 $x^{2}$ + 2x $\lt$3 -3 -3 $x^{2}$ + 2x -3 $\lt$0 2.) Factor the inequality (x-1)(x+3) $\lt$0 3.) Test numbers because the equation uses $\lt$0 we know we want our x-values to be negative: --Testing 0: ((0)-1)((0)+3) $\lt$0 = -3$\lt$0 --Testing -4:((-4)-1)((-4)+3) $\lt$0 =5$\lt$0 --Testing 2: ((2)-1)((2)+3) $\lt$0 =5$\lt$0 4.) Using this information we know the x interval is (-3,1) because that is when the values tested negative. Answer: (-3,1)
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