Introduction to Algebra

Algebra is great fun - you get to solve puzzles!

A Puzzle

What is the missing number?

OK, the answer is 6, right? Because 6 − 2 = 4. Easy stuff.

Well, in Algebra we don't use blank boxes, we use a letter (usually an x or y, but any letter is fine). So we write:

It is really that simple. The letter (in this case an x) just means "we don't know this yet", and is often called the unknown or the variable.

And when we solve it we write:

Why Use a Letter?

Because:

• it is easier to write "x" than drawing empty boxes (and easier to say "x" than "the empty box").
• if there are several empty boxes (several "unknowns") we can use a different letter for each one.

How to Solve

Algebra is just like a puzzle where we start with something like "x − 2 = 4" and we want to end up with something like "x = 6".

But instead of saying "obviously x=6", use this neat step-by-step approach:

• Work out what to remove to get "x = ..."
• Remove it by doing the opposite (adding is the opposite of subtracting)
• Do that to both sides

Here is an example:

We want
to remove
the "−2"

To remove it, do
the opposite, in
this case add 2

Do it to
both sides

Which is ...

Solved!

Why did we add 2 to both sides?

To "keep the balance"...

In Balance

Add 2 to Left Side

Out of Balance!

Add 2 to Right Side Also

In Balance Again

Just remember this:

See this in action at the Algebra Balance Animation.

Another Puzzle

What we want is an answer like "x = ...",
but the +5 is in the way of that!
We can cancel out the +5 with a −5 (because 5−5=0)

Have a Try Yourself

Now practice on this Simple Algebra Worksheet and then check your answers. Try to use the steps we have shown you here, rather than just guessing!

Try the questions below, then read Introduction to Algebra - Multiplication