Question

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

Answer 1

`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`