Introduction to Algebra
Algebra is great fun - you get to solve puzzles!
A Puzzle
What is the missing number?| − | 2 | = | 4 |
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:
| x | − | 2 | = | 4 |
And when we solve it we 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 are several empty boxes (several "unknowns") we can use a different letter for each one. |
So x is simply better than having an empty box. We aren't trying to make words with it!
And it doesn't have to be x, it could be y or w ... or any letter or symbol we like.
And it doesn't have to be x, it could be y or w ... or any letter or symbol we like.
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
We want
to remove
the "−2"
to remove
the "−2"
To remove it, do
the opposite, in
this case add 2
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 |
| To keep the balance, what we do to one side of the "=" we should also do to the other side! |
Another Puzzle
Solve this one:| x | + | 5 | = | 12 |
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)
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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