SOLUTION: -5126= -6 -5(3x+22)^5/3

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Question 697747: -5126= -6 -5(3x+22)^5/3
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I believe the exponent is %285%2F3%29, so I would write it as
-5126= -6 -5(3x+22)^(5/3) or -5126=+-6+-5%283x%2B22%29%5E%285%2F3%29
Since I cannot get those fractional exponents properly rendered, I'll try writing it as
-5126=+-6+-5%283x%2B22%29^(5/3)
We add 6 to both sides to get
-5120=+-5%283x%2B22%29^(5/3)
We multiply both sides times %28-1%29 because I do not like minus signs.
(It's an old grudge from when one minus sign michieviously turned into a plus sign as I transcribed apolynomial to the flip side on the second page of a very long multi-part problem in an 11th grade midterm).
Multiplying times %28-1%29 we get
5120=+5%283x%2B22%29^(5/3)
We divide both sides by 5 to get
1024=+%283x%2B22%29^(5/3)
You know that 1024=2%5E10 , right?
Using that, we re-write the equation as
2%5E10=+%283x%2B22%29^(5/3)
We cube both sides of the equal sign to get
%282%5E10%29%5E3=+%28%283x%2B22%29%5E%285%2F3%29%29%5E3 --> 2%5E30=%283x%2B22%29%5E5 --> %282%5E6%29%5E5=%283x%2B22%29%5E5 --> 2%5E6=3x%2B22 --> 64=3x%2B22
The rest is easy.
64=3x%2B22 --> 64-22=3x --> 42=3x --> 42%2F3=3x%2F3 --> highlight%28x=14%29