Expert: Scott A Wilson - 12/17/2009

Question
Here is the problem:
                 
                 -5
                 ___(16x-24)=35
                  8


Do you invert the fraction before solving the portion in parenthesis?  The answer is -2 but I dont know how to arrive at that answer




                  8

Answer
An easier way to write this would have been as (-5/8)(16X-24) = 35.
An even better way would have been -5(16x-24)/8 = 35.
I like to move everything that is in the denominator
all the way to the right side of the expression.

Yet that was just in how it is easy for me to right things clearly.

To solve, multiply both sides by the inverse, which is -8/5.
Since (-8/5)(-5/8) = 1, the left side become 16x-24.
Now (-8/5)35 = -8*7 = -56.

Thus, we now have 16x - 24 = -56.

Adding 24 to both sides gives 16x - 24 + 24 = -56 + 24.
That reduces to 16x = 32.

At last, divide both sides by 16.  In other words, the answer is 32/16,
and I'll leave that to you.


A little more
--------------------------------
Or I'll says that 32=2^5 and 16=2^4, so it is 2^5/2^4 = 2^1.
Anything to the one is the number itself.


A little weird
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The numbers were zero and one in the discussion of powers.
According to zero, all numbers need to be conformed to the same thing, and that is 1.
According to one, they should all be left alone.
In this way, it demonstrates that n^0 = 1 and n^1 = n.

Now if anybody bigger (and tougher) than one comes in,
he thinks the numbers should be moved farther from 1.

If anyone smaller than one comes in, he thinks they should be made closer to one.

Now when zero comes in to look at zero, he freaks out since he is looking at himself.
Since he freaked out, one is also freaked out and
sends himself out as a limit of the whole thing.