Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 3 - Solving Inequalities - 3-7 Absolute Value Equations and Inequalities - Practice and Problem-Solving Exercises: 25

Answer

$f=-2$ or $f=1.5$

Work Step by Step

$|4f+1|-2=5\longrightarrow$ add 2 to each side $|4f+1|-2+2=5+2\longrightarrow$ add $|4f+1|=7\longrightarrow$ definition of absolute value $4f+1=-7$ or $4f+1=7\longrightarrow$ solve each equation $4f+1=-7\longrightarrow$ subtract 1 from each side $4f+1-1=-7-1\longrightarrow$ subtract $4f=-8\longrightarrow$ divide each side by 4 $4f\div4=-8\div4\longrightarrow$ divide $f=-2$ OR $4f+1=7\longrightarrow$ subtract 1 from each side $4f+1-1=7-1\longrightarrow$ subtract $4f=6\longrightarrow$ divide each side by 4 $4f\div4=6\div4\longrightarrow$ divide $f=1.5$
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