Hey Fractal,

Great questions - as soon as I saw your subject line here I wanted to take a look, because understanding what you can and can't do with inequalities can be critical on a lot of these problems.

Addition/Subtraction to both sides

You can do this all day long, just like you would with an equation. Subtracting y from both sides like you did here was perfect, and probably the most useful way to simplify this one:

2y > y

subtract y from both sides

y > 0

As long as you do the same thing to both sides, you can add/subtract all you want with inequalities.



Multiplying/Dividing by a known value

Again, you can do this all day, as long as you know that:

-Multiply/Divide by a positive value ---> Keep the direction of the inequality the same (like you did)
-Multiply/Divide by a negative value ---> You MUST change the direction of the inequality

Here, 2y > y

divide both sides by 2, which is positive so you keep the sign the same direction

y > y/2 (strategically this doesn't add too much value, but you can definitely still do it)



Multiplying/Dividing by an unknown value

If you don't know the sign (positive/negative) of the variable, you cannot multiply/divide by it. Instead, you can subtract and then factor:

2y > y

subtract y from both sides:

2y - y > 0

Then factor out a y:

y (2-1) > 0

y > 0

And you can avoid the process of multiplying/dividing by a negative while still isolating the variable.



Great questions - I hope that helps...with inequalities, beware the potential of a negative multiplication/division term!