How do you simplify 6n-4+n?

1 Answer
Oct 25, 2016

6n-4+n=color(green)(7n-4)

Explanation:

Combine terms with identical variable components:
6n-4+n
color(white)("XXX")=6n+n-4

color(white)("XXX")=7n-4

Things you might have had problems with:

[1] Note that -4+n != -(4+n)
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 6n+n = 7n

Think of it in concrete terms:
color(white)("XXX")Suppose we have boxes of yoyos.
color(white)("XXX")We know every box has the same number of yoyos although we are not sure how many this is.
color(white)("XXX")Since we don't know how many there are in each box, we just call this number n.
color(white)("XXX")Then 6 boxes of yoyos would be 6xxn (commonly written as 6n) yoyos.
color(white)("XXX")If we add another box of yoyos we would have 7 boxes (each with n yoyos) for a total of 7xxn (or 7n) yoyos.