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: 22

Answer

(-$\infty$,-1) U (1,$\infty$)

Work Step by Step

1.) Set what the inequality equals to what it originally equals, and then set it to the opposite of that number with the opposite inequality sign $x^{2}$ + 2x$\gt$2 and $x^{2}$ + 2x$\lt$-2 2.) Solve the first inequality for x by subtracting 2 from both sides and factoring. $x^{2}$ + 2x$\gt$2 -2 -2 $x^{2}$ + 2x - 2$\gt$0 $(x-1)^{2}$$\gt$0 3.) Solve the first inequality for x by taking the square root of both sides and adding 1 $(x-1)^{2}$$\gt$0 x-1$\gt$0 +1 +1 x$\gt$1 4.) Identify the interval of x values the inequality is identifying x$\gt$1 5.) Solve the second inequality for x by adding two to both sides and factoring. $x^{2}$ + 2x$\lt$-2 +2 +2 $x^{2}$ + 2x+2$\lt$0 $(x+1)^{2}$$\gt$0 6.) Solve the first inequality for x by taking the square root of both sides and subtracting 1 $(x+1)^{2}$$\gt$0 x+1$\gt$0 -1 -1 x$\gt$-1 7.) Identify the interval of x values the inequality is identifying x$\gt$-1 8.)Combine the two intervals using a union. (-$\infty$,-1) U (1,$\infty$)
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