# How do you solve 7(5a-4)-1=14-8a?

Feb 27, 2017

See the entire solution process below:

#### Explanation:

First, expand the term in parenthesis on the left side of the equation by multiplying each term within the parenthesis by $\textcolor{red}{7}$:

$\left(\textcolor{red}{7} \times 5 a\right) - \left(\textcolor{red}{7} \times 4\right) - 1 = 14 - 8 a$

$35 a - 28 - 1 = 14 - 8 a$

$35 a - 29 = 14 - 8 a$

Next, add $\textcolor{red}{29}$ and $\textcolor{b l u e}{8 a}$ to each side of the equation to isolate the $a$ term while keeping the equation balanced:

$35 a - 29 + \textcolor{red}{29} + \textcolor{b l u e}{8 a} = 14 - 8 a + \textcolor{red}{29} + \textcolor{b l u e}{8 a}$

$35 a + \textcolor{b l u e}{8 a} - 29 + \textcolor{red}{29} = 14 + \textcolor{red}{29} - 8 a + \textcolor{b l u e}{8 a}$

$43 a - 0 = 43 - 0$

$43 a = 43$

Now, divide each side of the equation by $\textcolor{red}{43}$ to solve for $a$ while keeping the equation balanced:

$\frac{43 a}{\textcolor{red}{43}} = \frac{43}{\textcolor{red}{43}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{43}}} a}{\cancel{\textcolor{red}{43}}} = 1$

$a = 1$