## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$equivalent$
$\bf{\text{Solution Outline:}}$ Use the properties of equality to solve each of the given equations, $5x-4=2x$ and $3x=4 .$ If the solutions are the same, then the equations are equivalent. $\bf{\text{Solution Details:}}$ Using the properties of equality to isolate the variable, the first equation is equivalent to \begin{array}{l}\require{cancel} 5x-4=2x \\\\ 5x-2x=4 \\\\ 3x=4 \\\\ x=\dfrac{4}{3} .\end{array} Using the properties of equality to isolate the variable, the second equation is equivalent to \begin{array}{l}\require{cancel} 3x=4 \\\\ x=\dfrac{4}{3} .\end{array} Since the solutions of both of the given equations are the same, then the equations are $\text{ equivalent .}$