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: 19

Answer

(-$\infty$,2) U (6,$\infty$)

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