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Solving an Algebraic Equation that Contains Multiplication (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 Multiplication?

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



In the equation above, the x represents a number. It is being multiplied by 2. In words, the equation means "2 times x equals 4". (Note: It could be written as 2 × x. But the × and the x would be easily confused, so it is just written 2x. The 2 is the coefficient of x.)

To solve the equation, we have to find the number that, when you times it by 2, equals 4.

How to Solve the Algebraic Equation that Contains Multiplication

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 to multiplication is division, 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 multiplication.
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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 TOP TO BOTTOM

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



If the division shown in the bottom equation is rewritten as a fraction, the two steps become:





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

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 top, alongside the x on the left hand side of the equals sign, to being on the bottom, underneath the 4 on the right hand side of the equals sign.

The reverse can also be done. If there is a division, with one number shown underneath another term in a fraction, that bottom number can swap to the other side of the equals sign if it also moves up to the top.