Answer
$(7,\infty)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
\dfrac{3x-1}{4}\gt5
,$ use the properties of inequality.
For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$
For graphing inequalities, use a hollowed dot for the symbols $\lt$ or $\gt.$ Use a solid dot for the symbols $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
4\cdot\dfrac{3x-1}{4}\gt4\cdot5
\\\\
3x-1\gt20
\\\\
3x\gt20+1
\\\\
3x\gt21
\\\\
x\gt\dfrac{21}{3}
\\\\
x\gt7
.\end{array}
The red graph is the graph of the solution set.
In interval notation, the solution set is $
(7,\infty)
.$
