Answer
$t=-\dfrac{1}{12}$
Work Step by Step
Using the properties of equality, the value of the variable that satisfies the given expression, $
t+\dfrac{1}{3}=\dfrac{1}{4}
,$ is
\begin{array}{l}\require{cancel}
t=\dfrac{1}{4}-\dfrac{1}{3}
\\\\
t=\dfrac{3}{12}-\dfrac{4}{12}
\\\\
t=\dfrac{3-4}{12}
\\\\
t=\dfrac{-1}{12}
\\\\
t=-\dfrac{1}{12}
.\end{array}