Equations: Overview

Working with equations is an important step in laying the foundation for algebra. Look at this equation: 2 + 6 = . This equation is an open mathematical sentence. The box represents an unknown value. The box can be replaced by another symbol such as . Now the equation becomes 2 + 6 = . The value of the box in the first equation and that of the triangle in the second equation is 8. You could also write the equation as 2 + 6 = . The box, triangle, and blank are variables. A letter such as x is often used as a variable. The variable can appear in the middle of an equation, too—for example, 3 + x = 8.
In an equation, the equals sign indicates that the quantities on each side of the sign must be equal. Students can think of an equation as a balance, with the equals sign as the balance point.

Both sides of the balance must equal the same thing at all times for the pans to balance. Notice that the scales above are balanced because each pan has a five on it. Now look at the next figure.

This scale is also balanced, because the total on each side is 5. This balance shows the equation 4 + 1 = 5.

It is important to understand that we want to keep the pans balanced. If we added 2 to the left pan above, the left side would go down while the right side would go up, since 4 + 1 + 2 (which equals 7) is greater than (or heavier than) 5.

But if we added 2 to both pans, the scales would remain balanced since both sides would yield a sum of 7.

Students can think of the center bar as the equals sign. A key rule for working with equations is that you can add the same number to each side, subtract the same number from each side, and multiply or divide each side by the same number and the sides will stay equal. You must, however, do exactly the same operation to each side, or the equation will become unbalanced.