Answer
$t =-\dfrac{1}{10}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\dfrac{1}{6}t-\dfrac{3}{4}=t-\dfrac{2}{3}
,$ remove first the fraction by multiplying both sides by the $LCD.$ Then use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
The $LCD$ of the denominators, $\{
6,4,1,3
\},$ is $
12
$ since this is the least number that can be evenly divided (no remainder) by all the denominators. Multiplying both sides by the $LCD,$ the given equation is equivalent to
\begin{array}{l}\require{cancel}
12\left( \dfrac{1}{6}t-\dfrac{3}{4} \right)=12\left( t-\dfrac{2}{3} \right)
\\\\
2t-9 =12t-8
.\end{array}
Using the properties of equality to isolate the variable, the equation above is equivalent to
\begin{array}{l}\require{cancel}
2t-9 =12t-8
\\\\
2t-12t =-8+9
\\\\
-10t =1
\\\\
t =\dfrac{1}{-10}
\\\\
t =-\dfrac{1}{10}
.\end{array}
