 Suppose we have an expression. We can evaluate the expression by resolving all of the operations. This gives us something that should be the same as the original expression just in a different form. For example, let's say I want to evaluate 5 plus 7. The operation is addition, so we can add and we have 5 plus 7 is the same as 12. And remember, equals means replaceable, so we can write 5 plus 7 equals 12. How about evaluating 3x plus 5 when x equals 2? So remember, equals means replaceable. Now it's a good rule in math and in life that you can never write too much. So what we might do is start out with the blazingly obvious idea that 3x plus 5 is the same as 3x plus 5. Equals means replaceable, so this x equals 2 means that everywhere we see an x, we can replace it with 2. Since we'd like to be able to say what 3x plus 5 is, let's only replace the x on this side, so we'll replace this x with the 2. And we should throw it in a set of parentheses to make everything sensible. And now we have a bunch of arithmetic operations which we can then resolve. We could try to do this with more than one variable, so let's evaluate 3x plus 7y when x equals 2 and y equals negative 1. So equals means replaceable. Everywhere we see x, we'll replace it with 2. And everywhere we see y, we'll replace it with negative 1. And then we can evaluate the arithmetic operations to get our final answer.