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When
we started working with X's we had problems like this ... |
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3X - 5 = 0
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Then
we solved for X. |
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Now,
we are going to look at ... |
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3X - 5 = ?
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Instead
of a zero, we've got a question mark on the right side. |
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Here
the game is, feed in a number for X |
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and
see what the ? turns out to be. |
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If
X = 2, then ... |
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3(2)
- 5 = ? |
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6
- 5 = ? |
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1
= ? |
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So
when X = 2, the question mark equals 1. |
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If
X = -7, then ... |
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3(-7)
- 5 = ? |
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-21
- 5 = ? |
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-26
= ? |
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We
can chose anything that we want for X |
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and
then figure out what the question mark is. |
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Before
when we had a question mark in the problems, |
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math
people said: |
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"Yuk, we
can't have a question mark in an equation."
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"that
looks terrible!" |
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"Use
an "X" instead" |
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Guess
what, |
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math
types still don't like question marks in equations. |
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X
is already busy, so they got the next best thing. |
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So
what's next to X ? |
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Y
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So
instead of writing ... |
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3X - 5 = ?
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We
write ... |
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3X - 5 = Y
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But
it means the same thing! |
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So
now when we choose 2 as the value of X (X = 2), |
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we
get ... |
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3(2)
- 5 = Y |
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6
- 5 = Y |
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1
= Y |
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When
we choose -7 for X (X = -7) |
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we
get ... |
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3(-7)
- 5 = Y |
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-21
- 5 = Y |
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-26
= Y |
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OK,
I know it's not a big change, |
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but
sometimes math people are easily amused. |
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We
could be here until the end of time |
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choosing
values for X and seeing what we get for Y, |
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but
life's too short. |
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We
need a new way to look at this kind of equation. |
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Maybe
we could just have something that we could look at, |
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and
know that if X was this then Y was that |
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without
having to do the math for each and every number. |
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We
need to be able to see the BIG PICTURE. |
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POP
QUIZ |
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Guess
what's on the next page? |
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copyright 2005 Bruce Kirkpatrick |
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