Algebra Tutor

What is algebra? Algebra is a branch of mathematics concerning the study of structure, relation, and quantity

 

Need help with your Algebra homework?

Algebra can seem quite daunting at first. Suddenly there are X’s and Y’s popping up all over the place where previously you just had numbers. You may have heard from other people – friends, family etc that it’s really hard and complicated to get your head around but that’s nonsense. Algebra is really quite simple once you understand the basic concept. If you're looking for Algebra help, check out our Algebra tutorial to get yourself ahead of the pack!

At the heart of algebra are variables. Variables are containers that can change value or that represent a fixed value. You may be used to sums that look like:

 

3 + 3 = 6

If you wrote instead:

 

3 + X = 6 (where we’ve just replaced the second 3 with an X)

 

You can immediately see that X must equal 3.

 

Here are some for you to work out. We’ll go through the solutions next: 

 

1)  14 – X = 7

2)  12/X = 4

3) 2*X = 9

 

An easy way of finding out the value that X represents is by rearranging the equation.  Rearranging these equations is easy. All you need to do is perform the same mathematical operation on each side of the equation. For the problems above:

 

1:

 

 14 – X = 7

Subtract  14 from both sides:

14-X-14 = 7-14

Cancel out the values:

-X = -7

So X = 7

2:

 

12/X = 4

Multiply by X:

12 = 4X

Divide by 4:

3 = X or X=3

 

3:

 

2*X = 9

Divide by 2:

X = 4.5

 

That’s really all there is to it! Although as the complexity increases and the number of variables increases so does the problem of finding out what the possible values are. 

 

Simultaneous Equations:

 

If we have:

 

X + Y = 6

Then there are an infinite number of solutions to this equation:

 1 + 5  =  6

 2 + 4 = 6

 1.1 + 4.9 =  6

Etc.

To find a fixed set of values we’d need another equation involving X and Y. Say we had:

 

X + Y = 6

 

and:

 

X  - Y = 4

 

We can then combine the two equations by  adding the left parts and the right parts of the equation together:

 

X+Y+(X-Y) = 6+4

 

So:

 

 X+X = 10

2X = 10

X=10/2

 

So X = 5

Then substituting this back into the first equation:

 

5+Y=6

 

So Y = 1.

 

X=5 and Y=1 is the only way to make X+Y=6 and X-Y=4.  Pretty cool huh?!

 

Algebra is a major area of mathematics and is extremely useful in engineering, computer science, financial modelling and research. A good understanding of algebra will repay you for a lifetime.