Tutoring math, you realize the importance of this technique.  The math tutor introduces it as an essential skill for those learning algebra.

Most people are fairly comfortable with solving an equation such as

2x -11 = 7x + 19

By adding and subtracting quantities to both sides, you “get all the x terms to one side, and get all the numbers to the other side.”

First, we might add 11 to both sides in order to get rid of the -11:

2x = 7x + 30

We might next subtract 7x from both sides in order to get rid of the 7x:

-5x=30

Finally, we divide both sides by -5:

x=-6

With a new question, let’s “take it to the next level”:

3x/5 +1 = x – 3/2

The fractions’ presence makes this question higher level than the last, since a new technique is needed. Specifically, we must clear out the fractions, by the following steps:

Step 1

Identify the smallest number that both 5 and 2 divide into. The answer is 10.

Step 2

Multiply each term on both sides by the answer from Step 1 (10, in our case):

10(3x/5) +10(1) = 10x – 10(3/2)

Step 3

Cancel where possible. For instance,

10(3x/5)=30x/5=6x

On the non-fraction terms, there is no cancellation; we just mulitply them by 10.

The results of mulitplying each term by 10:

6x + 10 = 10x – 15

We are back to the more familiar situation. From here, we might subtract 10 from both sides

6x = 10x -25

Next, we’ll subtract 10x from both sides

-4x=-25

Finally, we’ll divide both sides by -4:

x=-25/-4=25/4

Answers can be – and often are – fractions.

I’ll be discussing algebra further in coming posts:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.