# How do you solve (16.5+3t)/3=(0.9-t)/-5?

Feb 20, 2017

See the entire solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{15}$ to eliminate the fractions while keeping the equation balanced:

$\textcolor{red}{15} \times \frac{16.5 + 3 t}{3} = \textcolor{red}{15} \times \frac{0.9 - t}{- 5}$

$\cancel{\textcolor{red}{15}} 5 \times \frac{16.5 + 3 t}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} = \cancel{\textcolor{red}{15}} \left(- 3\right) \times \frac{0.9 - t}{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 5}}}}$

$5 \left(16.5 + 3 t\right) = - 3 \left(0.9 - t\right)$

Next, expand the terms within parenthesis:

$\left(5 \times 16.5\right) + \left(5 \times 3 t\right) = \left(- 3 \times 0.9\right) - \left(- 3 \times t\right)$

$82.5 + 15 t = - 2.7 + 3 t$

Then, subtract $\textcolor{b l u e}{82.5}$ and $\textcolor{red}{3 t}$ from each side of the equation to isolate the $t$ term while keeping the equation balanced:

$82.5 + 15 t - \textcolor{b l u e}{82.5} - \textcolor{red}{3 t} = - 2.7 + 3 t - \textcolor{b l u e}{82.5} - \textcolor{red}{3 t}$

$82.5 - \textcolor{b l u e}{82.5} + 15 t - \textcolor{red}{3 t} = - 2.7 - \textcolor{b l u e}{82.5} + 3 t - \textcolor{red}{3 t}$

$0 + 12 t = - 85.2 + 0$

$12 t = - 85.2$

Now, divide each side of the equation by $\textcolor{red}{12}$ to solve for $t$ while keeping the equation balanced:

$\frac{12 t}{\textcolor{red}{12}} = - \frac{85.2}{\textcolor{red}{12}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{12}}} t}{\cancel{\textcolor{red}{12}}} = - 7.1$

$t = - 7.1$

Feb 20, 2017

$t = - 7.1$

#### Explanation:

$\frac{16.5 + 3 t}{3} = \frac{0.9 - t}{-} 5$

multiply both sides by-15

$\therefore - 15 \frac{\left(16.5 + 3 t\right)}{3} = - 15 \frac{\left(0.9 - t\right)}{-} 5$

$\therefore - 5 \left(16.5 + 3 t\right) = 3 \left(0.9 - t\right)$

$\therefore - 82.5 - 15 t = 2.7 - 3 t$

$\therefore - 15 t + 3 t = 2.7 + 82.5$

$\therefore - 12 t = 85.2$

$\therefore - t = \frac{85.2}{12}$

$\therefore t = - \frac{85.2}{12}$

$\therefore t = - 7.1$

check:

substitute$t = - 7.1$

$\frac{\left(16.5 + 3 \left(- 7.1\right)\right)}{3} = \frac{\left(0.9 - \left(- 7.1\right)\right)}{-} 5$

$\therefore \frac{16.5 - 21.3}{3} = \frac{0.9 + 7.1}{- 5}$

$\therefore - \frac{4.8}{3} = \frac{8}{-} 5$

$\therefore - 1.6 = - 1.6$