# How do you solve (3t)/2+7=4t-3?

Jan 14, 2017

See full solution process below:

#### Explanation:

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

$\textcolor{red}{2} \left(\frac{3 t}{2} + 7\right) = \textcolor{red}{2} \left(4 t - 3\right)$

$\frac{\textcolor{red}{2} \times 3 t}{2} + \left(\textcolor{red}{2} \times 7\right) = \left(\textcolor{red}{2} \times 4 t\right) - \left(\textcolor{red}{2} \times 3\right)$

$\frac{\cancel{\textcolor{red}{2}} \times 3 t}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} + 14 = 8 t - 6$

$3 t + 14 = 8 t - 6$

Next, add and subtract the necessary terms from each side of the equation to isolate the $t$ terms on one side of the equation and the constants on the other side of the equation while keeping the equation balanced:

$3 t + 14 - \textcolor{red}{3 t} + \textcolor{b l u e}{6} = 8 t - 6 - \textcolor{red}{3 t} + \textcolor{b l u e}{6}$

$3 t - \textcolor{red}{3 t} + 14 + \textcolor{b l u e}{6} = 8 t - \textcolor{red}{3 t} - 6 + \textcolor{b l u e}{6}$

$0 + 14 + \textcolor{b l u e}{6} = 8 t - \textcolor{red}{3 t} - 0$

$20 = \left(8 - 3\right) t$

$20 = 5 t$

Now, divide each side of the equation by $\textcolor{red}{5}$ to solve for $t$ while keeping the equation balanced:

$\frac{20}{\textcolor{red}{5}} = \frac{5 t}{\textcolor{red}{5}}$

$4 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} t}{\cancel{\textcolor{red}{5}}}$

$4 = t$

$t = 4$

Jan 14, 2017

$t = 4$

#### Explanation:

We can 'eliminate' the fraction in the equation by multiplying ALL terms on both sides by 2, the denominator of the fraction term.

$\left(\cancel{2} \times \frac{3 t}{\cancel{2}}\right) + \left(2 \times 7\right) = \left(2 \times 4 t\right) - \left(2 \times 3\right)$

$\Rightarrow 3 t + 14 = 8 t - 6$

subtract 8t from both sides.

$3 t - 8 t + 14 = \cancel{8 t} \cancel{- 8 t} - 6$

$\Rightarrow - 5 t + 14 = - 6$

subtract 14 from both sides.

$- 5 t \cancel{+ 14} \cancel{- 14} = - 6 - 14$

$\Rightarrow - 5 t = - 20$

To solve for t, divide both sides by - 5

$\frac{\cancel{- 5} t}{\cancel{- 5}} = \frac{- 20}{- 5}$

$\Rightarrow t = 4 \text{ is the solution}$