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Solving an Algebraic Equation that Contains Division (Mathematics Lesson)

What Is Algebra?

Algebra is using letters (or other symbols) to represent an unknown number.

An equation that uses algebra is called an algebraic equation. (Note: algebraic is the adjective for algebra.)

What Is an Algebra Equation that Contains Division?

An algebraic equation that contains division is an equation with at least one letter being used to represent a number which is itself divided by another number.



In the equation above, the x represents a number. It is being divided by 2. In words, the equation means "x divided by 2 equals 3".

To solve the equation, we have to find the number that, when you divide it by 2, equals 3.

How to Solve the Algebraic Equation that Contains Division

Question: What is the value of x in the equation below?



General Approach:

The key to solving an algebraic equation is to isolate the letter (or symbol) you are trying to find the value of.

This is done by rearranging the equation so that you just have x on the left-hand side of the equals sign, and the answer on the right-hand side.

In mathematics, you want to rearrange:



so you just have x on the left-hand side of the equals sign, and the answer on the right-hand side:



The key to rearranging an algebraic equation is:

Whatever you do to one side of an equation, you must do to the other side!

Step-by-Step Approach:

Step 1
Look at what has been done to the x.



Step 2
Find the opposite thing to get x on its own.

The opposite of division is multiplication, as shown in the table of opposites below:



The opposite of ÷2 is ×2:

Step 3
Do this to both sides of the equals sign.




This is the solution:



The slider below gives another example of solving an algebraic equation that contains division.
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Note

THE GOLDEN RULE OF ALGEBRA

The golden rule of algebra is:

Whatever you do to one side of an equation, you must do to the other side!

Think of a pair of scales. The equals signs means that both sides of the scales balance:



If you do anything to just one side, the scales no longer balance and the equality no longer holds:



If you do the same thing to both sides, the scales return to balance, and the equality holds once again:



SWAP THE SIDES, SWAP BOTTOM TO TOP

Compare two of the steps in the step-by-step solution given on this page:



You can think of this of as 'switching sides, switching bottom to top'.

The 2 has moved from the left hand side to the right hand side of the equals sign.

It has also changed from being on the bottom, underneath the x, to being on the top, multiplying the 2.

The reverse can also be done. If there is a multiplication, with one number multiplying a term, such as the unknown x; that number can swap to the other side if it also moves down to the bottom, underneath any terms on the top.