Answer
$\left\{\dfrac{4}{5}\right\}$
Work Step by Step
Using $a(b+c)=ab+ac$ or the Distributive Property, the given equation, $
7-(4+3t)+2t=-6(t-2)-5
,$ is equivalent to
\begin{align*}
7-1(4)-1(3t)+2t&=-6(t)-6(-2)-5
\\
7-4-3t+2t&=-6t+12-5
.\end{align*}
By combining like terms and using the properties of equality, the equation above is equivalent to
\begin{align*}\require{cancel}
(7-4)+(-3t+2t)&=-6t+(12-5)
\\
3-t&=-6t+7
\\
-t+6t&=7-3
\\
5t&=4
\\\\
\dfrac{\cancel5t}{\cancel5}&=\dfrac{4}{5}
\\\\
t&=\dfrac{4}{5}
.\end{align*}
Hence, the solution set of the equation $
7-(4+3t)+2t=-6(t-2)-5
$ is $\left\{\dfrac{4}{5}\right\}$.
