In junior high school you probably remember solving word problems like [GS]:
Mary has twice as many apples as John. Mary throws half her apples away, because they are rotten, and John eats one of his. Mary still has twice as many apples as John. How many apples did Mary and John have initially?
You solved this word problem by introducing variables, m and j, to stand for the number of apples Mary initially has and the number of apples John initially has, respectively; then you wrote two equations to relate the two numbers:
Then you solved for m and j to find a solution to the problem.
In the process of solving for m and j you used properties
about
=, e.g.,
moving quantities from one side of the = sign to the other.
I am going to remind you of these properties in this handout.
You also used properties about
-, 
, and /; these are called algebraic
properties; more on this later.