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

1 Answer
Oct 25, 2016

Answer:

#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.