Answer
equivalent
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequalities,
\begin{array}{l}\require{cancel}
-4x-1\le15
\\\text{and}\\
-4x\le16
.\end{array}
If the solutions are the same, then the given inequalities are equivalent.
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the solution of the first inequality is
\begin{array}{l}\require{cancel}
-4x-1\le15
\\\\
-4x\le15+1
\\\\
-4x\le16
\\\\
\dfrac{-4x}{-4}\le\dfrac{16}{-4}
\\\\
x\ge-4
.\end{array}
Using the properties of inequality, the solution of the second inequality is
\begin{array}{l}\require{cancel}
-4x\le16
\\\\
\dfrac{-4x}{-4}\le\dfrac{16}{-4}
\\\\
x\ge-4
.\end{array}
Since the solutions of both inequalities are the same, then the given inequalities are $\text{
equivalent
.}$
