Linear Equations

A linear equation is also called a first-degree equation. It can be as simple as x + 1 =  2 to as complicated as ½(x + 3) – ¼(x + 5) = ¾(x – 7). In order to solve the complicated ones, we have to know how to solve simple ones first. The following are four very simple (a.k.a. one-step) linear equations: 

1) x + 2 = 7          2) x – 3 = 9          3) x × 4 = 8          4) x ÷ 6 = 5

To solve the above equations, we use inverse operations. Needless to say, the inverse operation of addition is subtraction. For subtraction, the inverse operation is addition. Similarly, multiplication and division are inverse operations of each other. Furthermore, if we do one thing on one side of the equation, we have to do the same thing on the other side of the equation. Therefore, to solve x + 2 = 7, we minus 2 on both sides, which yields x = 5. That is,

      x + 2 = 7

x + 2 – 2 = 7 – 2

            x = 5