# How do you solve -5n-8(1+7n)=-8?

Sep 29, 2017

$n = 0$

#### Explanation:

$- 5 n - 8 \left(1 - 7 n\right) = - 8$
Open the brackets
$- 5 n - 8 + 56 n = - 8$
$- 5 n - 8 + 56 n + 8 = - 8 + 8$
$51 n = 0$
$n = 0$

Sep 29, 2017

$n = 0$

#### Explanation:

$\text{distribute bracket and collect like terms}$

$- 5 n - 8 - 56 n = - 8$

$\Rightarrow - 61 n - 8 = - 8$

$\text{add 8 to both sides}$

$- 61 n \cancel{- 8} \cancel{+ 8} = - 8 + 8$

$\Rightarrow - 61 n = 0$

$\Rightarrow n = 0$

$\textcolor{b l u e}{\text{As a check}}$

Substitute this value into the equation and if both sides are equal then it is the solution.

$\text{left "=0-8(1+0)=0-8=-8=" right}$

$\Rightarrow n = 0 \text{ is the solution}$

Sep 29, 2017

$n = 0$

#### Explanation:

$- 5 n - 8 \left(1 + 7 n\right) = - 8$

Expanding:
$- 5 n - 8 \left(1\right) - 8 \left(7 n\right) = - 8$
$= - 5 n - 8 - 56 n = - 8$

$= - 5 n \cancel{- 8} \cancel{+ 8} - 56 n = \cancel{- 8} \cancel{+ 8}$
$= 61 n = 0$
$\frac{\cancel{61} n}{\cancel{61}} = \frac{0}{61} = 0$
$\Rightarrow n = 0$