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Simple algebra hints and tips

What is algebra? Algebra is performing maths that, rather than having specific numbers in it, contains generalised operations using symbols.

For instance:

2 + 3 = 5 is a non-algebraic sum.

But if we have:

2 + x = 5, then we have a simple algebraic sum.

As soon as non-integer variables get entered into the equation, a lot of people and maths students enter a cold sweat and panic at these unfamiliar terms.

However, they need not do.

The single key to understanding algebra and being able to work out the answer is the ability to manipulate or REARRANGE AN ALGEBRAIC EQUATION.

Now, let's look at an example and work out the answer:

4 + x = 12. What is x?

Now, remember that 'x' is a variable here, so it could represent anything. One way to relate algebra to the real world is to substitute 'x' for something meaningful. So we can think of this equation as saying:

"If I have four apples, how many more apples do I need to have in order to get twelve apples in total".

As soon as re write that, we realise we have a very simple sum and can move straight to the answer.

But if the sum was a little more complicated, this also helps us work out the next step: how to re-arrange the equation.

If I have 4 apples, how many more do I need to get 12?

This is the same as 'If I have 12 apples and I eat 4 of them, how many do I have left?'

Now we have a simple sum: 12 - 4 = 8, and so the answe r is 8. We have re-arranged the equation and solved the algebraic sum!

Let's look at a slightly trickier one:

2x + 6 = 18

The key to re-arranging an equation is that WHATEVER YOU DO TO ONE SIDE, YOU MUST DO TO THE OTHER.

Here we want to work out what 'x' is. So first we want to get rid of the 6 from the left hand side, so we subtract it FROM BOTH SIDES OF THE EQUATION.

This leaves us with:

2x + 6 - 6 = 18 - 6, a very simple sum telling us that:

2x = 12

Using our visualisation technique, this means "How many apples do I need to have that when I add the same number again I have twelve in total?"

Now, since we are dealing with Multiplication, to get to a single x, we need to Divide. To get from two to one, we divide both sides by two, giving us this:

2x / 2 = 12 / 2 (the '/' means divide)

This gives us:
x = 6

And that's the answer!
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