Question

How do you solve `-5 > -5-3w`?

Answer 1

`w>0`

Explanation:

Right from the start, you can say that you need `w` to be positive because any negative value of `w` would make the product `(-3 * w)` positive, which in turn will make the right-hand side of the inequality bigger than `(-5)`.

SInce you need the left-hand side of the inequality to be strictly greater than the right-hand side, you cannot have `w=0`, since that would imply that

`-5 > -5 - 3 * 0`

`-5color(red)(cancel(color(black)(>)))-5`

So, the solution set for this inequality is `w>0`.

`-5 > -5 - 3w`

`-color(red)(cancel(color(black)(5))) + color(red)(cancel(color(black)(5))) > -3w`

`0 > -3w implies w > 0`