Question

How do you evaluate `5( 2n + 1) = 7( 5n + 3) + 9`?

Answer 1

See the entire solution process below:

Explanation:

First, expand the terms in parenthesis on each side of the equation:

`(5 xx 2n) + (5 xx 1) = (7 xx 5n) + (7 xx 3) + 9`

`10n + 5 = 35n + 21 + 9`

`10n + 5 = 35n + 30`

Next, subtract `color(red)(10n)` and `color(blue)(30)` from each side of the equation to isolate the `n` terms while keeping the equation balanced:

`10n + 5 - color(red)(10n) - color(blue)(30) = 35n + 30 - color(red)(10n) - color(blue)(30)`

`10n - color(red)(10n) + 5 - color(blue)(30) = 35n - color(red)(10n) + 30 - color(blue)(30)`

`0 - 25 = 25n + 0`

`-25 = 25n`

Now, divide each side of the equation by `color(red)(25)` to solve for `n` while keeping the equation balanced:

`-25/color(red)(25) = (25n)/color(red)(25)`

`-1 = (color(red)(cancel(color(black)(25)))n)/cancel(color(red)(25))`

`-1 = n`

`n = -1`