Question

How do you solve `-3(7n+3)<6n`?

Answer 1

See the entire solution process below:

Explanation:

First, expand the term in parenthesis:

`-3(7n + 3) < 6n`

`-21n - 9 < 6n`

Now, add `color(red)(21n)` to each side of the inequality to isolate the `n` term while keeping the inequality balanced:

`-21n - 9 + color(red)(21n) < 6n + color(red)(21n)`

`-21n + color(red)(21n) - 9 < (6 + 21)n`

`0 - 9 < 27n`

`-9 < 27n`

Next, divide each side of the inequality by `color(red)(27)` to solve for `n` while keeping the inequality balanced:

`-9/color(red)(27) < (27n)/color(red)(27)`

`-1/3 < (color(red)(cancel(color(black)(27)))n)/cancel(color(red)(27))`

`-1/3 < n`

And to solve in terms of `n` we reverse or "flip" the inequality:

`n > -1/3`