# How do you solve 5/2t-t=3+3/2t?

Jan 14, 2017

See entire solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{2}$ to eliminate the fraction and keep the equation balanced:

$\textcolor{red}{2} \left(\frac{5}{2} t - t\right) = \textcolor{red}{2} \left(3 + \frac{3}{2} t\right)$

$\left(\textcolor{red}{2} \times \frac{5}{2} t\right) - \left(\textcolor{red}{2} \times t\right) = \left(\textcolor{red}{2} \times 3\right) + \left(\textcolor{red}{2} \times \frac{3}{2} t\right)$

$\left(\cancel{\textcolor{red}{2}} \times \frac{5}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} t\right) - 2 t = 6 + \left(\cancel{\textcolor{red}{2}} \times \frac{3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} t\right)$

$5 t - 2 t = 6 + 3 t$

$3 t = 6 + 3 t$

We can now subtract $\textcolor{red}{3 t}$ from each side of the equation:

$3 t - \textcolor{red}{3 t} = 6 + 3 t - \textcolor{red}{3 t}$

$0 = 6 + 0$

$0 \ne 6$

Because $0$ does not equal $6$ we know there is no solution for $t$ for this problem other than the null set or $t = \left\{\emptyset\right\}$