Answer
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 $\text{
equivalent equations
.}$
