Equations

The sign = means is equal to. In other words, there is exactly the same amount on both sides of the = sign.

For example, 3 + 7 = 10. There are ten on each side of the equation because 3 + 7 is ten. The solution to an equation is based on that same consideration. Both sides must have exactly the same amount.

4 + _ = 9

Which number fits into the blank space? Many will find the missing number to be five. Because 4 + 5 = 9. It is equal on both sides.

But guessing is not a very good way to solve an equation, so we need the right tools to achieve this. We can modify the equation as long as we remember that, whatever we do, we must do it to both sides of the equation. See examples 1 and 2.

Also, we note that addition cancels subtraction and multiplication cancels division. In other words, if we count two plus one, we get three. To get back to the original number, we subtract one from three.

If we multiply a number by another number, we can revert back by dividing by the same number.

Example 3.

Solve the equation 3x + 2 = 8

3x + 2 = 8 || -2

3x + 2-2 = 8-2

3x = 6 ||: 3

x = 6/3

x = 2

So the goal is to eliminate all the numbers around x so that only x is left.