Reviewing Algebraic Manipulations

During your year in Chemistry you will regularly be solving equations for variables. To make the process go a little smoother, here is a "brush-up" sheet on basic algebraic manipulations.

Isolating Variables:
•When you need to isolate a variable in an equation, you may accomplish this by changing both sides of the "=" sign exactly the same way, for example:

1. If 5x + 4 = 29, what is "x"?
   1. subtract 4 from both sides of the "=" sign
      1. 5x + 4 - 4=29-4
      2. 5x=25
   2. divide both sides of the "=" sign by 5
      1. 5x/5=25/5
      2. x=5
2. If y/3 - 2 = 2
   1. add 2 to each side of the "=" sign
      1. y/3 - 2 + 2 = 2 + 2
      2. y/3=4
   2. multiply each side of the "=" sign by 3
      1. y/3 x 3 = 4 x 3
      2. y = 12