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!
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
Looking for GMAT practice questions? Try out the Veritas Prep Question Bank.
Learn More.
