Using the Principles Together

Suppose you were given an equation like

 

2x – 3 = 5.

 

You will need to use the addition principle to move the –3, and the multiplication principle to remove the coefficient 2. Which one should you use first? Strictly speaking, it does not matter—you will eventually get the right answer. In practice, however, it is usually simpler to use the addition principle first, and then the multiplication principle. The reason for this is that if we divide by 2 first we will turn everything into fractions:

 

Given: 2x – 3 = 5

 

Suppose we first divide both sides by 2:

 

Now there is nothing wrong with doing arithmetic with fractions, but it is not as simple as working with whole numbers. In this example we would have to add 3/2 to both sides of the equation to isolate the x. It is usually more convenient, though, to use the addition principle first:

 

Given: 2x – 3 = 5

 

Add 3 to both sides:

 

 

 

 At this point all we need to do is divide both sides by 2 to get x = 4.