Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 2 - Section 2.1 - Linear Equations in One Variable - Exercise Set: 32

Answer

$z=-\frac{1}{2}$

Work Step by Step

We are given that $\frac{2z+7}{8}-2=z+\frac{z-1}{2}$. First, we can multiply each term by 8. Since this is the least common denominator of each term, this will eliminate all fractions from the equation. $\frac{2z+7}{8}\times8-2\times8=z\times8+\frac{z-1}{2}\times8$ $2z+7-16=8z+4\times(z-1)$ Use the distributive property to simplify the right side. $2z+7-16=8z+4z-4$ Group like terms on both sides. $2z-9=12z-4$ Add 9 to both sides. $2z=12z+5$ Subtract 12z from both sides. $-10z=5$ Divide both sides by -10. $z=-\frac{1}{2}$
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