How do you solve 8( 1+ 7n ) = 8( - 2+ 6n )?

Jan 21, 2018

Solving for $n$,

$n = 3$

Explanation:

To solve algebraically for $n$, we must isolate $n$. To do this, we perform a sequence of operations. Each time we perform an operation, we do it on both sides of the equality, so that we don't destroy the equality (if you only do something to one side, the original equality will no longer be true).

So, first expand the brackets

$8 \left(1 + 7 n\right) = 8 \left(- 2 + 6 n\right)$

$\Rightarrow 8 + 56 n = - 16 + 48 n$

Next, subtract $48 n$ from both sides to get $n$ on one side only

$8 + 56 n - \textcolor{b l u e}{48 n} = - 16 + 48 n - \textcolor{b l u e}{48 n}$

$\Rightarrow 8 + 8 n = - 16$

Now, subtract 8 from both sides

$8 + 8 n - \textcolor{b l u e}{8} = - 16 - \textcolor{b l u e}{8}$

$\Rightarrow 8 n = - 24$

Finally, divide both sides by 8 to isolate $n$

$8 n \div \textcolor{b l u e}{8} = - 24 \div \textcolor{b l u e}{8}$

$\Rightarrow n = - 3$

Now you should go back to the question and substitute $n = - 3$ into each side of the equality separately and see if they both give the same answer. If they don't, you have the wrong $n$ value.