Question

How do you solve `3-6n-4<17`?

Answer 1

`n > -3`

Explanation:

`3-6n-4 < 17`

Simplify the left hand side:
`-1 - 6n < 17`

Add `color(blue)(6n)` to both sides of the inequality:
`-1 - 6n quadcolor(blue)(+quad6n) < 17 quadcolor(blue)(+quad6n)`

#-1 < 17 + 6n

Subtract `color(blue)17` from both sides:
`-1 quadcolor(blue)(-quad17) < 17 + 6n quadcolor(blue)(-quad17)`

`-18 < 6n`

Divide both sides by `color(blue)6`:
`(-18)/color(blue)6 < (6n)/color(blue)6`

`-3 < n`

`n > -3`

This can be said as "`n` is greater than `-3`."

(mathwarehouse.com)

The open circle on the `-3` means that `-3` is not a solution (but anything greater than it).

Hope this helps!

Answer 2

`n> -3`

Explanation:

We can simplify left side to `-1-6n`. We now have

`-1-6n<17`

Next, we can add `1` to both sides to get

`-6n<18`

Lastly, divide both sides by `6` to isolate `n`. Recall that since we divided by a negative, the sign flips. We're left with

`n> -3`

Hope this helps!