You can
put this solution on YOUR website!Let x= unknown number
To find out what's going on, we have to translate this sentence into an algebraic expression:
First let's square the unknown number to get
Now subtract 1 to get
Divide the result by that number minus 1 (ie
) to get
Now subtract the original number x to get
So the sentence translates to
. Now let's simplify:
Start with the given expression
Factor
into
by using the difference of squares
Cancel like terms
Simplify
Group like terms
Combine like terms
So
simplifies to
. In other words,
for any x but
. Can you see why?
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As for your own number game, you could try...
Take any number, square it, and add 6 multiplied by the original number. After that add 5. Now divide this by the original number plus one. Now subtract your original number to get 5.
This long sentence translates to ( tell me if you need help with the translation)
Factor
to get
Cancel like terms
Simplify
Group like terms
Combine like terms
So
simplifies to
. In other words,
for any x but
. Can you see why?
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