# How do you simplify 6n-4+n?

Oct 25, 2016

$6 n - 4 + n = \textcolor{g r e e n}{7 n - 4}$

#### Explanation:

Combine terms with identical variable components:
$6 n - 4 + n$
$\textcolor{w h i t e}{\text{XXX}} = 6 n + n - 4$

$\textcolor{w h i t e}{\text{XXX}} = 7 n - 4$

Things you might have had problems with:

[1] Note that $- 4 + n \ne - \left(4 + n\right)$
Standard evaluation is from left to right, so the $4$ is subtracted but the $n$ is added (without the parentheses).

[2] Sometimes when starting out people have trouble seeing why $6 n + n = 7 n$

Think of it in concrete terms:
$\textcolor{w h i t e}{\text{XXX}}$Suppose we have boxes of yoyos.
$\textcolor{w h i t e}{\text{XXX}}$We know every box has the same number of yoyos although we are not sure how many this is.
$\textcolor{w h i t e}{\text{XXX}}$Since we don't know how many there are in each box, we just call this number $n$.
$\textcolor{w h i t e}{\text{XXX}}$Then $6$ boxes of yoyos would be $6 \times n$ (commonly written as $6 n$) yoyos.
$\textcolor{w h i t e}{\text{XXX}}$If we add another box of yoyos we would have $7$ boxes (each with $n$ yoyos) for a total of $7 \times n$ (or $7 n$) yoyos.