Solving an equation is like solving a puzzle! It means finding a value for the variable that makes the equation true. Using the properties of real numbers that you've learned, you can rearrange the terms of an equation and use inverse operations to help you find the value of the variable. But be careful! You can think of an equation like a balance scale—whatever you do to one side of the scale, you must also do to the other side, to keep it in balance.

First, let's look at a simple addition equation, x + 15 = 30.

To solve the equation we must try to get the variable x alone on one side. We can use the inverse of adding 15 - or subtracting 15 - to get x alone on the left side. Now we have x alone on the left side, since 15 – 15 = 0, but the scale is not in balance. To balance the scale, we must also subtract 15 from the right side of the equation.

x + 15 - 15 = 30 - 15
         x = 15

30 – 15 = 15, so we find that x = 15.

We can check this solution by substituting the value 15 for x in the original equation. When we evaluate for x = 15 we get 30 = 30, which is a true statement. We know our solution is correct!

      x + 15 = 30
(15) + 15 = 30
                             30 = 30 Correct!

Now, let's look at a subtraction equation, y – 9 = 3

To solve this equation we must try to get the variable y alone on one side. We can use the inverse of subtracting 9, or adding 9, to get y alone on the left side.

y - 9 + 9 = 3 + 9
   y - 0 = 12
        y = 12

Now we have y alone on the left side, since –9 + 9 = 0, but the scale is not in balance. To balance the scale, we must also add 9 to the right side of the equation.

Now we have y alone on the left side of the equation. Three plus nine is twelve, so we find that y = 12.

We can check this solution by substituting the value 12 for y in the original equation. When we evaluate for y = 12, we get 3 = 3, which is a true statement. Our solution is correct!

      y - 9 = 3
(12) - 9 = 3
                          3 = 3 Correct!

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