Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 6 - Algebra: Equations and Inequalities - 6.4 Linear Inequalities in One Variable - Exercise Set 6.4 - Page 384: 70


\[x\ge \frac{7+48y}{6}\].

Work Step by Step

Given is an inequality \[Ax+By\le C;A<0\], where \[A,B,C\] are constants. An equivalent inequality can be found by substituting any values for \[A,B,C\], which also fulfills the condition \[A<0\]. Use the property of inequality, which says that an inequality changes the sign if divided by a negative quantity. An equivalent inequality can be written as follows: \[-6x+48y\le -7\] This inequality is restructured with \[x\] isolated on left side as: \[\begin{align} & x\ge \frac{-7-48y}{-6} \\ & x\ge \frac{7+48y}{6} \\ \end{align}\] The equivalent inequality is given as \[x\ge \frac{7+48y}{6}\].
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