-2(2y + 5) < -2(y - 9)

Solve it just like you would if there were an equal sign = instead
of an inequality sign < until you get to the step when you divide or
multiply both sides by something.   

Distribute to remove the parentheses:

-2(2y + 5) < -2(y - 9)
  -4y - 10 < -2y


Add 2y to both sides to get the y-term off the right side:

  -4y - 10 < -2y
  +2y        +2y
  --------------
  -2y - 10 <   0

Add +10 to both sides to get the term without a y off the left side:

   -2y - 10 <  0
       + 10  +10
   -------------
   -2y      < 10

Now this is where solving inequalities are different from 
solving equations.  

If you divide or multiply both sides by a NEGATIVE number, you
must change the direction (reverse) of the inequality.  So when 
we divide both sides of the above by -2, since -2 is a NEGATIVE 
number, we must change the < to >

        y > -10

Note:  It is just as important for other inequalities that you
may have to solve, that you remember this:  When you divide or multiply
both sides by a POSITIVE number you DO NOT reverse the inequality sign!  
JUST DON'T get the idea that you always reverse the inequality sign.  
You reverse it when but ONLY WHEN(!) you divide or multiply through by 
a NEGATIVE number.

To graph that solution on a number line:

------------o================================================================>
-12  -11  -10   -9   -8   -7   -6   -5   -4   -3   -2   -1    0    1    2    3

The interval notation for this solution set is [-10,)

Edwin