Answer
$t=\dfrac{2}{5}$
Work Step by Step
Multiplying both sides by the $LCD=
15
$, then the solution to the given equation, $
\dfrac{2}{3}+4t=6t-\dfrac{2}{15}
$, is
\begin{array}{l}
5(2)+15(4t)=15(6t)-1(2)
\\\\
10+60t=90t-2
\\\\
60t-90t=-2-10
\\\\
-30t=-12
\\\\
t=\dfrac{-12}{-30}
\\\\
t=\dfrac{2}{5}
.\end{array}
CHECKING:
\begin{array}{l}
\dfrac{2}{3}+4\cdot\dfrac{2}{5}=6\cdot\dfrac{2}{5}-\dfrac{2}{15}
\\\\
\dfrac{2}{3}+\dfrac{8}{5}=\dfrac{12}{5}-\dfrac{2}{15}
\\\\
\dfrac{10}{15}+\dfrac{24}{15}=\dfrac{36}{15}-\dfrac{2}{15}
\\\\
\dfrac{34}{15}=\dfrac{34}{15}
\text{ (TRUE)}
.\end{array}
Hence, the solution is $
t=\dfrac{2}{5}
$.
