#### Answer

$\left( -\infty,\dfrac{49}{2} \right]$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
\dfrac{3}{5}(t-2)-\dfrac{1}{4}(2t-7)\le3
,$ use the Distributive Property and 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 Distributive Property and the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
20\left( \dfrac{3}{5}(t-2)-\dfrac{1}{4}(2t-7)\right)\le20(3)
\\\\
12(t-2)-5(2t-7)\le60
\\\\
12(t)+12(-2)-5(2t)-5(-7)\le60
\\\\
12t-24-10t+35\le60
\\\\
12t-10t\le60+24-35
\\\\
2t\le49
\\\\
t\le\dfrac{49}{2}
.\end{array}
The red graph is the graph of the solution set.
In interval notation, the solution set is $
\left( -\infty,\dfrac{49}{2} \right]
.$