Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.7 Inequalities - 1.7 Exercises - Page 159: 34


$\color{blue}{(\frac{1}{6}, 1)}$

Work Step by Step

Subtract $3$ to each part: \begin{array}{ccccc} &2-3&\gt &-6x+3-3 &\gt &-3-3 \\&-1 &\gt &-6x &\gt &-6 \end{array} Divide each part by $-6$. Note that since a negative number is divided to the inequality, the inequality symbol will be reversed. \begin{array}{ccccc} \\&\frac{-1}{-6} &\lt &\frac{-6x}{-6} &\lt &\frac{-6}{-6} \\&\frac{1}{6} &\lt &x &\lt &1 \end{array} Thus, the solution to the given inequality is: $\color{blue}{(\frac{1}{6}, 1)}$
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