Think of equations as a type of balance where the left side must balance with the right side.  We can manipulate the sides by adding, subtracting, multiplying or dividing but we can't change the value of one side without doing the same thing to the other side.  In class, we often say "BOTH SIDES" when talking about equations.

• For instance, you could say that 2 * 7 = 14 but we could also say that 2 * 7 = 7 + 7.  This is a definition of multiplying by two but it is also a use of an equation.  In this case, we just rewrote it, we didn't change a value. 
• We could also say that since 2 * 7 = 14, then 2 * 7 + 5 = 14 + 5 by adding 5 to both sides.
• Of course, some things don't really help us: 2 * 7 * 0 = 14 * 0 but how does that help solve anything?

Some things to remember ...

• your answer is found when you isolate the variable
• you "undo" by working backwards
• your equation must remain balanced at all steps
• addition and subtraction are inverse operations
• multiplication and division are inverse operations

Sometimes an equation really looks like it takes one-step.  For instance, what number would you subtract 7 from to get 12?  Of course, that number is 19, that is just an addition fact..   But this is also a good chance to show what equations are.  Both sides have the same value and that must be true for every step.  So, in order to solve a subtraction problem where we know the answer (difference) but we are missing one of the parts, we really add.

In the equation where we multiply a number by 5, add 6 to that and get 21, you may not be able to do that in your head.  But, we know that we need to write as an equation so we can see what to do:  5x + 6 = 21 Note that we would put in a value for x, multiply that by 5 and add 6.  We "undo" in reverse order.  Subtract 6 (from both sides) and then divide by 5 (both sides.)