How do you solve #-77=n-4(3-3n)# using the distributive property?

1 Answer
Alan P.
Aug 9, 2017

#n=-5#
(see below for application of distributive property)

Explanation:

Using the distributive property (in general):
#color(white)("XXX")color(red)(a)(b+c)=(color(red)ab+color(red)ac)#
and
#color(white)("XXX")(d+e)color(blue)f=(dcolor(blue)f+ecolor(blue)f)#

Given
#-77=n-color(red)4(3-3n)#
#color(white)(-77)=n-(color(red)4xx3-color(red)4xx3n)color(white)("xxxx")#[distributive property]
#color(white)(-77)=n-(12-12n)#
#color(white)(-77)=n-12+12n#
#color(white)(-77)=13n-12#
...adding #12# to both sides:
#-65=13n#
...dividing both sides by #13#
#-5=ncolor(white)("xxx")"or"color(white)("xxx")n=-5#

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