Algebra is about using letters as well as numbers. A lot of maths uses equations as you probably know from school. Equations are a mix of letters and numbers. At school, you are probably given equations to "solve" and they sometimes scare people as they don't know what to do with them. I would like to start with the very simplest equations so that you understand them and can feel confident with them.

**Here is a very simple equation:-**

*x* = 3

We are giving *x* the value 3.

So two lots of *x* must be 6. We write this as :-

2*x* = 6

(This is the same as *x* + *x* = 6)

And three lots of x must be 9. (I hope you know your times tables!)

3*x* = 9

(This is the same as *x* + *x* + *x* = 9)

In algebra, we are allowed to miss out the times, X, sign. So instead of saying 2 X *x* = 6 and 3 X *x* = 9

we just write 2*x* = 6 and 3*x* = 9.

We can keep going through the 3 times table, making more equations, like this:

4*x* = 12, 5*x* = 15, 6*x* = 18, 7*x* = 21, 8*x* = 24,

9*x* = 27, 10*x* = 30, 11*x* = 33, 12*x* = 36.

All these equations rely on *x* being equal to 3.

Let's take one of these equations and see what else we can do. We will choose 7*x* = 21

Now let's add a 1 to the 7*x* : 7*x* + 1

If we do this, we must add 1 to the other side too so that it balances:-

7*x* + 1 = 21 + 1

And we simplify this to 7*x* + 1 = 22.

If a teacher gave you 7*x* + 1 = 22 to "solve", you might wonder what to do. But you have seen how easy it is by the work we have just done.

So, we subtract the "+1" from both sides:-

7*x* + 1 -1 = 22 - 1

7*x* = 21

To "solve" the equation just means to find the value of* x* . We already know it is 3, but if you didn't know that you would do the following:-

7*x* = 21

*x* = 21/7 or *x* = 21 รท 7

(We divide by the 7 so that we can find what one *x* is equal to.)

As long as you know your tables, you can then write

*x* = 3

And now you have solved the equation 7*x* + 1 = 22,

since (7 X 3) + 1 = 22. Easy, wasn't it!

**Next we will use x = 5**

See if you can work out what has happened in these two equations:-

*x* + 1 = 6 and *x* + 4 = 9

The first one has had 1 added to the *x* and to the 5 and the second one has had 4 added to the *x* and to the 5.

If *x* = 5 then we can also say that 2*x* = 10 and we can add first 1 and then 4 to give the following equations:-

2*x* + 1 = 11 and 2*x* + 4 = 14

It is true that 4*x* = 20 if *x* = 5 and, again, we can add first 1 and then 4 and we get the following:-

4*x* + 1 = 21 and 4*x* + 4 =24

Let's add some other numbers to these equations to get some variety (always remember that here *x* = 5) :-

*x* + 6 = 11

*x* + 10 = 15

*x* + 16 = 21

*x* + 18 = 23

2*x* + 5 = 15

2*x* + 9 = 19

2*x* + 12 = 22

2*x* + 13 = 23

4*x* + 6 = 26

4*x* + 8 = 28

4*x* + 11 = 31

4*x* + 19 = 39

So far we have been adding to the equation *x* = 5 so now let's subtract:-

*x* - 1 = 4

*x* - 3 = 2

2*x* - 1 = 9

2*x* - 3 = 7

4*x* - 1 = 19

4*x* - 3 = 17

*x* - 4 = 1

*x* - 5 = 0

2*x* - 5 = 5

2*x* - 7 = 3

4*x* - 8 = 12

4*x* - 17 = 3

Now let's take one of these equations and see what we need to do to get back to *x* = 5 :-

4*x* - 1 = 19

Add 1 to both sides:-

4*x* - 1 + 1 = 20

4*x* = 20

*x* = 20/4

*x* = 5

I hope that you have followed this introduction to equations. If there is something you don't understand then please email us on randmgibson@aol.com