Equations with Added Variables

X - 7 = 14

In order to solve an equation with a variable, we need to make the expressions have the same value. Here, clearly X cannot equal 14 because 14 - 7 would be “7”. So how do we make the “X” equal “14”?

In a variable equation we must either add or subtract the known number in the unknown expression. In the above equation the unknown expression is “X - 7”. As this shows the number “7” is being subtracted from “X” we must add 7 to 7 as follows:

X - 7 + 7

We must then do the equal math to the known express of “14” as follows:

14 + 7

The new equation will now look as follows:

X - 7 + 7 = 14 + 7

We now add 14 + 7 = 21 and that makes the value of “X” equal 21.

21 - 7 = 14 so X = 21

However, sometimes we are faced with a different variable such as 8X - 2 = 14. When we see this type of equation, we will need to take a number of steps. First we must add the known number in the unknown expression to itself, or: 8X - 2 + 2 and we must also add 2 to the known expression, i.e., 14 + 2. The equation will now look like the following:

8X - 2 + 2 = 14 + 2
8X - 2 + 2 = 8X
14 + 2 = 16
8X = 16

At this point we must then divide the number in the unknown express with the number in the known expression and then multiply the number found in the unknown expression with the answer. For example:

8X = 16 becomes X = 16 ÷ 8
16 ÷ 8 = 2
8 x 2 = 16
X = 2