Chapter 9 - Inequalities and Problem Solving - 9.1 Inequalities and Applications - 9.1 Exercise Set: 10

equivalent inequalities

Work Step by Step

$\bf{\text{Solution Outline:}}$ Solve the solution sets of the given statements, \begin{array}{l}\require{cancel} -\dfrac{1}{3}t\le-5 \\\text{and}\\ t\ge15 .\end{array} If the solution sets are the same, then they are equivalent. Otherwise, they are not equivalent. $\bf{\text{Solution Details:}}$ Using the properties of inequality, the solution of the first inequality is \begin{array}{l}\require{cancel} -\dfrac{1}{3}t\le-5 \\\\ -3\left( -\dfrac{1}{3}t \right)\le-3(-5) \\\\ t\ge15 .\end{array} Since this is the same as second given inequality, then the given are $\text{ equivalent inequalities .}$

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