Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.9 - Linear Inequalities and Absolute Value Inequalities - Exercise Set - Page 140: 138

Answer

The statement is false. Inequality $3x>6$ is not equivalent to $2>x$; rather, it is equivalent to $x>2$.

Work Step by Step

Let us consider the following inequality: $3x>6$ Now, solve the above inequality for x as follows: First, divide both sides of the inequality by 3, $\begin{align} & \frac{3x}{3}>\frac{6}{3} \\ & x>2 \end{align}$ We know that dividing the inequality by a positive number does not affect the inequality. Therefore, dividing the above inequality by 3 does not affect the inequality. Thus, the statement is false. $3x>6$ is not equivalent to $2>x$; rather, it is equivalent to $x>2$.
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