Introduction to Algebra
A Puzzle
What is the missing number?
| - | 2 | = | 4 |
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 would write:
x | - | 2 | = | 4 |
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 you solve it you write:
x | = | 6 |
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 were several empty boxes (several "unknowns") we can use a different letter for each one. |
How to Solve
Algebra is just like a puzzle where you start with something like "x-2 = 4" and you 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! |
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Solve this one:
x | + | 5 | = | 12 |
Start with: | x + 5 = 12 |
What you are aiming for is an answer like "x = ...", and the plus 5 is in the way of that! If you subtract 5 you can cancel out the plus 5 (because 5-5=0) |
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So, let us have a go at subtracting 5 from both sides: | x+5 -5 = 12 -5 |
A little arithmetic (5-5 = 0 and 12-5 = 7) becomes: | x+0 = 7 |
Which is just: | x = 7 |
| Solved! |
(Quick Check: 7+5=12) |
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