## The Lesson

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 Algebraic 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 This Equation

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

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:

## 1

Look at what has been done to the x.

## 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:

The opposite of ×2 is ÷2:

## 3

Do this to both sides of the equals sign.

## 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!**

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.

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