#### Answer

$t=15$

#### Work Step by Step

Using the properties of equality, the solution to the given equation, $
\dfrac{3}{5}t-1=8
$, is
\begin{array}{l}
\dfrac{3}{5}t=8+1
\\\\
\dfrac{3}{5}t=9
\\\\
t=9\left( \dfrac{5}{3} \right)
\\\\
t=15
.\end{array}
Checking:
\begin{array}{l}
\dfrac{3}{5}(15)-1=8
\\\\
9-1=8
\\\\
8=8
\text{ (TRUE)}
.\end{array}
Hence, the solution is $
t=15
.$