Question

How do you solve `15 + 6n = 7(2n + 3)`?

Answer 1

See the entire solution process below:

Explanation:

First, expand the term within parenthesis on the right side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

`15 + 6n = 7(2n + 3)`

`15 + 6n = (7 xx 2n) + (7 xx 3)`

`15 + 6n = 14n + 21`

Next, subtract `color(red)(6n)` and `color(blue)(21)` from each side of the equation to isolate the `n` term while keeping the equation balanced:

`15 + 6n - color(red)(6n) - color(blue)(21) = 14n + 21 - color(red)(6n) - color(blue)(21)`

`15 - color(blue)(21) + 6n - color(red)(6n) = 14n - color(red)(6n) + 21 - color(blue)(21)`

`-6 + 0 = 8n + 0`

`-6 = 8n`

Now, divide each side of the equation by `color(red)(8)` to solve for `n` while keeping the equation balanced:

`-6/color(red)(8) = (8n)/color(red)(8)`

`-6/8 = (color(red)(cancel(color(black)(8)))n)/cancel(color(red)(8))`

`-(2 xx 3)/(2 xx 4) = n`

`-(color(red)(cancel(color(black)(2))) xx 3)/(color(red)(cancel(color(black)(2))) xx 4) = n`

`-3/4 = n`

`n = -3/4`