Question

How do you solve `5> \frac { n } { 6} + 5> - 1`?

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(5)` from each segment of the system of inequalities to isolate the `n` term while keeping the system balanced:

`5 - color(red)(5) > n/6 + 5 - color(red)(5) > -1 - color(red)(5)`

`0 > n/6 + 0 > -6`

`0 > n/6 > -6`

Now, multiply each segment by `color(red)(6)` to solve for `n` while keeping the system balanced:

`color(red)(6) xx 0 > color(red)(6) xx n/6 > color(red)(6) xx -6`

`0 > cancel(color(red)(6)) xx n/color(red)(cancel(color(black)(6))) > -36`

`0 > n > -36`

Or

`n > -36` and `n < 0`

Or, in interval notation:

`(-36, 0)`