Are you ready for this week's work? Let's get started! This is another long lesson so you may need another cup of coffee

You probably remember that an equation involves an "equals sign", with a mix of variables and numbers. Solving the equation means figuring out what number (or numbers) work for the variable. You'll know that you are finished your algebra problem when you have the variable all by itself; for example, when you can write something like "x = 5."

A few simple rules will help you to solve basic algebra equations. The first is the rule of balancing. This rule states that you must always keep the left side of any equation balanced with, or equal in value to, the right side of an equation.

Remember that the equal sign ( = ) in any equation shows that the left side and right side are already equal in amount.

So when you do work on an equation to 'solve' it, you must make sure that whenever you decide to do a math operation (addition, subtraction, multiplication and division are all called operations) by a certain number (such as 'add 5' or 'divide by 22') on one side of an equation, you must do the same thing on the other side (such as 'add 5', or 'divide by 22'). This is the balancing rule that you must follow to keep the left and right sides equal at each step of your solution.

You will see lots of examples of using the balancing rule ahead, but here is one for you to look at now. Remember the example about Jim's meal at a restaurant from last week? He spent $25.50 in total for the dinner, but that included the$4.00 tip. The question asks you to find out the cost of the meal before the tip:

x + $4.00 =$25.50

In a minute you will learn the reason why, but for now, I am telling you that to find the value of
x (the cost of the meal before the tip) you will need to subtract $4 from the left hand side. By the rule of balancing, you now know that you will also have to do the same operation (subtraction) of the same number (4) on the right side too, to keep the two sides equal. Here is how it will look: x +$ 4.00 - $4.00 =$ 25.50 - $4.00 The problem still isn't solved all the way, but by the rule of balancing, the same$4 has been subtracted from both sides of this equation. This correctly follows the balancing law, and is the proper next step. Each step of solving any equation must stay balanced like this. You will have lots of practice following this rule of balancing.

The second rule involves "working with opposites." You probably already know that addition and subtraction are opposites.

"Doing the opposite" may seem odd at first, but it really does work! For example, have a look at this equation:

x + 5 = 7

To solve this one, you will want to get the variable (x) all by itself on the left side of the equation, but there is "+ 5" also on the left side to get rid of first. To get rid of the + 5 that is next to the x you need to subtract 5 from both sides of the equation (based on the balancing rule you just learned). It will look like this:

x + 5 - 5 = 7 - 5

The two 5's on the left side of the equation cancel out (because + 5 - 5 = 0). On the right side, you get 7 - 5 = 2. So you can re-write the equation like this:

x = 2

Now that you have x all by itself on one side of the equation, you know that you are done! Sure enough, if you replace the variable 'x' by the number '2', the equation is correct: 2 + 5 = 7