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-10+1/3y>2/3y

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You would solve this one just like a regular algebraic equation.  If it helps, change the problem (for now) into:

-10 + 1/3y = 2/3 y.    (Be sure that when you put the inequality back in it faces the right way.  More on that in a sec.)

So, we want to get all the y's on one side and all the rest of it on the other.  To do this, let's subtract 1/3 y from both sides, giving us.

-10 = 1/3y.  (The inequality symbol here would still be >= as we haven't changed much.)  

Last step is to get rid of that 1/3, so let's multiply both sides by 3.  We also need to put that inequality symbol back in.  So:

-30 >= y.  

Note: We can rewrite this so y is in front.  If we do, we need to swap the direction the inequality points as well.   (y <= -30)  Same goes for if you multiply/divide this whole inequality by a negative number.