How do you solve -6n-10=-2n+4(1-3n)?

Mar 30, 2017

$n = 1.75$

Explanation:

This might look a little intimidating, but the process is fairly straightforward.
To begin, let's distribute the $4$, so that the problem becomes $- 6 n - 10 = - 2 n + 4 - 12 n$.
From here, we should combine like-terms. That leaves us with
$- 6 n - 10 = - 14 n + 4$.

We need to isolate the variable, so our next step should be to move all the constants to one side and all the variables to the other.

$- 6 n - 10 = - 14 n + 4$
$\textcolor{g r e e n}{+ 14 n} \textcolor{w h i t e}{} \textcolor{p u r p \le}{+ 10} = \textcolor{g r e e n}{+ 14 n} \textcolor{w h i t e}{.} \textcolor{p u r p \le}{+ 10}$

Now we have $8 n = 14$, and if we divide by $8$ on both sides we have $n = \frac{14}{8}$ or $1.75$.

Mar 30, 2017

$n = \frac{7}{4}$

Explanation:

The first step is to distribute the bracket.

$\Rightarrow - 6 n - 10 = - 2 n + 4 - 12 n$

$\Rightarrow - 6 n - 10 = - 14 n + 4$

Collect terms in n on the left side and numeric values on the right side.

$- 6 n + 14 n - 10 = \cancel{- 14 n} \cancel{+ 14 n} + 4$

$\Rightarrow 8 n - 10 = 4$

$8 n \cancel{- 10} \cancel{+ 10} = 4 + 10$

$\Rightarrow 8 n = 14$

divide both sides by 8

$\frac{\cancel{8} n}{\cancel{8}} = \frac{14}{8}$

$\Rightarrow n = \frac{14}{8} = \frac{7}{4}$

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

Substitute this value into the equation and if the left side equals the right side then it is the solution.

$\text{left side } = \left(- 6 \times \frac{7}{4}\right) - 10 = - \frac{21}{2} - 10 = - \frac{41}{2}$

$\text{right side } = \left(- 2 \times \frac{7}{4}\right) + 4 \left(1 - 3 \times \frac{7}{4}\right)$

$\textcolor{w h i t e}{r i g h t s i \mathrm{de} \times} = - \frac{7}{2} + 4 \left(1 - \frac{21}{4}\right)$

$\textcolor{w h i t e}{r i g h t s i \mathrm{de} \times} = - \frac{7}{2} - 17 = - \frac{41}{2}$

$\Rightarrow n = \frac{7}{4} \text{ is the solution}$