# How do you solve 2( 9t - 1) + 3= 13?

Jun 10, 2017

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{3}$ from each side of the equation to isolate the term with parenthesis while keeping the equation balanced:

$2 \left(9 t - 1\right) + 3 - \textcolor{red}{3} = 13 - \textcolor{red}{3}$

$2 \left(9 t - 1\right) + 0 = 10$

$2 \left(9 t - 1\right) = 10$

Next, divide each side of the equation by $\textcolor{red}{2}$ to isolate the parenthesis while keeping the equation balanced:

$\frac{2 \left(9 t - 1\right)}{\textcolor{red}{2}} = \frac{10}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \left(9 t - 1\right)}{\cancel{\textcolor{red}{2}}} = 5$

$9 t - 1 = 5$

Then, add $\textcolor{red}{1}$ to each side of the equation to isolate the $t$ term while keeping the equation balanced:

$9 t - 1 + \textcolor{red}{1} = 5 + \textcolor{red}{1}$

$9 t - 0 = 6$

$9 t = 6$

Now, divide each side of the equation by $\textcolor{red}{9}$ to solve for $t$ while keeping the equation balanced:

$\frac{9 t}{\textcolor{red}{9}} = \frac{6}{\textcolor{red}{9}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{9}}} t}{\cancel{\textcolor{red}{9}}} = \frac{3 \times 2}{\textcolor{red}{3 \times 3}}$

$t = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} \times 2}{\textcolor{red}{\textcolor{b l a c k}{\cancel{\textcolor{red}{3}}} \times 3}}$

$t = \frac{2}{3}$