Answer
$t=\dfrac{16}{3}$
Work Step by Step
Multiplying both sides by the $LCD=
12
$, then the solution to the given equation, $
\dfrac{2}{3}+\dfrac{1}{4}t=2
$, is
\begin{array}{l}
4(2)+3(t)=12(2)
\\\\
8+3t=24
\\\\
3t=24-8
\\\\
3t=16
\\\\
t=\dfrac{16}{3}
.\end{array}
CHECKING:
\begin{array}{l}
\dfrac{2}{3}+\dfrac{1}{4}\cdot\dfrac{16}{3}=2
\\\\
\dfrac{2}{3}+\dfrac{4}{3}=2
\\\\
\dfrac{6}{3}=2
\\\\
2=2
\text{ (TRUE)}
.\end{array}
Hence, the solution is $
t=\dfrac{16}{3}
$.
