Question

How do you solve `0=4(n-4)-6(n-4)` using the distributive property?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each term with each parenthesis by the term outside the parenthesis:

`0 = color(red)(4)(n - 4) - color(blue)(6)(n - 4)`

`0 = (color(red)(4) xx n) - (color(red)(4) xx 4) - (color(blue)(6) xx n) - (color(blue)(6) xx -4)`

`0 = 4n - 16 - 6n - (-24)`

`0 = 4n - 16 - 6n + 24`

Next, on the right side of the equation, group and combine like terms:

`0 = 4n - 6n - 16 + 24`

`0 = (4 - 6)n + 8`

`0 = -2n + 8`

Then, subtract `color(red)(8)` from each side of the equation to isolate the `n` term while keeping the equation balanced:

`0 - color(red)(8) = -2n + 8 - color(red)(8)`

`-8 = -2n + 0`

`-8 = -2n`

Now, divide each side of the equation by `color(red)(-2)` to solve for `n` while keeping the equation balanced:

`(-8)/color(red)(-2) = (-2n)/color(red)(-2)`

`4 = (color(red)(cancel(color(black)(-2)))n)/cancel(color(red)(-2))`

`4 = n`

`n = 4`