# Chapter 9 - Inequalities and Problem Solving - 9.1 Inequalities and Applications - 9.1 Exercise Set: 5

equivalent equations

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Solve the solution sets of the given statements, \begin{array}{l}\require{cancel} 5x+7=6-3x \\\text{and}\\ 8x+7=6 .\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 equality, the solution of the first equation is \begin{array}{l}\require{cancel} 5x+7=6-3x \\\\ 5x+3x=6-7 \\\\ 8x=-1 \\\\ x=-\dfrac{1}{8} .\end{array} Using the properties of equality, the solution of the second equation is \begin{array}{l}\require{cancel} 8x+7=6 \\\\ 8x=6-7 \\\\ 8x=-1 \\\\ x=-\dfrac{1}{8} .\end{array} Since the solutions of both equations are the same, then they are $\text{ equivalent equations .}$

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