Question

How do you solve `42=-6(-3n+6)+6(n-3)` using the distributive property?

Answer 1

To solve this using the distributive property you multiply each term outside a set of parenthesis by each term inside the parenthesis it is associated with. See full explanation of the process below.

Explanation:

To solve this using the distributive property you multiply each term outside a set of parenthesis by each term inside the parenthesis it is associated with. We need to pay close attention to the signs of each term.

`42 = color(red)(-6)(color(blue)(-3n) + color(blue)(6)) + color(green)(6)(color(purple)(n) - color(purple)(3))`

`42 = (color(red)(-6) xx color(blue)(-3n)) + (color(red)(-6) xx color(blue)(6)) + (color(green)(6) xx color(purple)(n)) + (color(green)(6) xx color(purple)(-3))`

`42 = 18n - 36 + 6n - 18`

We can now group and combine like terms:

`42 = 18n + 6n - 36 - 18`

`42 = (18 + 6)n - 54`

`42 = 24n - 54`

We can now use normal algebra to solve for `n`:

`42 + color(red)(54) = 24n - 54 + color(red)(54)`

`96 = 24n - 0`

`96 = 24n`

`96/color(red)(24) = (24n)/color(red)(24)`

`4 = (color(red)(cancel(color(black)(24)))n)/cancel(color(red)(24))`

`4 = n`

`n = 4`