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: 20

Answer

(-$\infty$, -7/2) U (-1/2,$\infty$)

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 2x+4$\gt$3 and 2x+4$\lt$-3 2.) Solve the first inequality for x by subtracting 4 and dividing by 2 to both sides 2x+4$\gt$3 -4 -4 2x$\gt$-1 $\div$2 $\div$2 x$\gt$-1/2 3.) Identify the interval of x values the inequality is identifying x$\gt$-1/2 = (-1/2,$\infty$) 4.) Solve the second inequality for x by subtracting 4 and dividing by 2 to both sides 2x+4$\lt$-3 -4 -4 2x$\lt$-7 $\div$2 $\div$2 x$\lt$-7/2 5.) Identify the interval of x values the inequality is identifying x$\lt$-7/2 = (-$\infty$, -7/2) 6.)Combine the two intervals using a union. (-$\infty$, -7/2) U (-1/2,$\infty$)
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