Question

How do you solve `1/4n+12>=3/4n-4` and graph the solution on a number line?

Answer 1

`nle32`

Explanation:

add 4 to both sides
`1/4n+16le3/4n`
subtract `1/4n` from both sides
`16le1/2n`
divide `16` by `1/2`
it looks like this
`16/1 * 2/1`
your answer is `32`
so your final equation is `nle32`
on a number line, put a closed circle on 32 and draw the line going towards the negatives indefinitely.

Here is the graph

Answer 2

`n<=32`

Explanation:

`1/4 n + 12 >= 3/4 n - 4`
Let's start by subtracting `color(red)(3/4 n)` from both sides
`1/4 n + 12 - color(red)(3/4 n) >=cancel (3/4 n) - 4 cancelcolor(red)(-3/4 n)`
`(-1)/2 n + 12 >= -4`
Then, we can subtract `color(green)(12)` from both sides
`(-1)/2 n + cancel12 - cancelcolor(green)(12) >= -4 - color(green)(12)`
`(-1)/2 n >= -16`
In order to find `n`, we need to multiply both sides by `color(orange)(2/(-1))`
`color(orange)((2/-1))((-1)/2 n) >= color(orange)(2/-1)(-16)`
`cancel((-2)/-2 n) >= ((-32)/-1)`
`n <=32`