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Now let's get a little trickier ... |
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| I'm thinking of a number. | ||
| If you multiply the number by 3 you get 12. | ||
| What's the number? | ||
| Translated into X stuff, this is: | ||
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3 × X = 12 |
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| To save space, we write this as: | ||
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3X = 12 |
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| When you an X's, and it is multiplied by something (like 3) | ||
| you just write 3X and not 3 x X. | ||
| It's like, | ||
| if you had 3 apples, you'd just write "3 apples", | ||
| not "3 x apples". | ||
| OK, so we've got 3X = 12. | ||
| Adding or subtracting stuff won't help us here. | ||
| We need another way to get the X by itself. | ||
| Here it is: | ||
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| There is a 3 that is multiplied times the X. | ||
| So to get rid of it we divide both sides by 3 ... | ||
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| and simplify ... | ||
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| And a 1 in the denominator doesn't change anything | ||
| so we can get rid of them ... | ||
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X = 4 |
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| Swell, here's another one ... | ||
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7X = 35 |
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| So this time there is a 7 multiplied times the X | ||
| To get rid of it we divide both sides by 7 ... | ||
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| and then simplify ... | ||
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| This time, we didn't even bother to write the 1's | ||
| in the denominators. | ||
| Now an even trickier one ... | ||
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| This one might need some explaining ... | ||
| What we have been doing up to now, | ||
| is turning the number next to the X into 1. | ||
| That is, we multiply by whatever we need to, | ||
| to turn the number next to the X into a 1. | ||
| Here, the number next to the X is 1/3. | ||
| What do you multiply 1/3 by to get 1? | ||
| You need to multiply it by 3. | ||
| So ... | ||
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| We might also have a problem with X in it more than once. | ||
| We might have ... | ||
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3X + 2 - X = 12 |
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| So the first thing that you need to do | ||
| is to combine the 3X and the -X. | ||
| 3X - X = 2X | ||
| (it's like 3 apples minus 1 apple equals 2 apples) | ||
| So now we've got: | ||
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2X + 2 = 12 |
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| Now we need some subtraction ... | ||
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| and some division ... | ||
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| One last note: | ||
| Any time we have a number or an X or things | ||
| multiplied together, it is called a term. | ||
| So these are all terms: | ||
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3X 4 -5 -12X |
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| These are NOT: | ||
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3X + 5 3 - X |
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| Those last two were two terms each. | ||
| Terms are usually separated from each other | ||
| by a plus or minus sign. | ||
|
copyright 2005 Bruce Kirkpatrick |
