# How do you solve -232= 6( - 7n + 3) - 8n?

Mar 7, 2018

See a solution process below:

#### Explanation:

First, expand the terms in the parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis. Then group and combine common terms:

$- 232 = \textcolor{red}{6} \left(- 7 n + 3\right) - 8 n$

$- 232 = \left(\textcolor{red}{6} \times - 7 n\right) + \left(\textcolor{red}{6} \times 3\right) - 8 n$

$- 232 = - 42 n + 18 - 8 n$

$- 232 = - 42 n - 8 n + 18$

$- 232 = \left(- 42 - 8\right) n + 18$

$- 232 = - 50 n + 18$

Next, subtract $\textcolor{red}{18}$ from each side of the equation to isolate the $n$ term while keeping the equation balanced:

$- 232 - \textcolor{red}{18} = - 50 n + 18 - \textcolor{red}{18}$

$- 250 = - 50 n + 0$

$- 250 = - 50 n$

Now, divide each side of the equation by $\textcolor{red}{- 50}$ to solve for $n$ while keeping the equation balanced:

$\frac{- 250}{\textcolor{red}{- 50}} = \frac{- 50 n}{\textcolor{red}{- 50}}$

$5 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 50}}} n}{\cancel{\textcolor{red}{- 50}}}$

$5 = n$

$n = 5$

Mar 7, 2018

$n = 5$

#### Explanation:

−232=6 ("-"7n+3)−8n      Solve for $n$

1) Clear the parentheses by distributing the $6$
After you have multiplied both of the terms inside the parentheses by 6, you will have this:
- 232 = - 42 n + 18 - 8n

2) Combine like terms
After you combine -42 n with $- 8 n$, you will get this
-232 = -50 n + 18

3) Subtract $18$ from both sides to isolate the -50  n term
-250 = - 50 n

4) Divide both sides by $- 50$ to isolate $n$
$5 = n$

$n = 5$

$\textcolor{w h i t e}{m m m m m m}$ ――――――――

Check

Sub in $5$ in the place of $n$ in the original equation

−232=6 ("-"7 n  +3)−8 n
−232=6 ("-"7(5)+3)−8(5)

1) Multiply   $\text{-} 7 \left(5\right)$  inside the parentheses
−232=6 (-35+3)−8(5)

2) Combine $- 35$ with $3$ inside the parentheses
−232=6  (-32)−8(5)

3) Clear the parentheses by distributing the $6$ and the $8$
-232  = -192 - 40

4) Combine like terms
-232  = -232

$C h e c k$