If #x+15=10#, what is #x^3-x^-2+16x^-1#?

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Answer 1 · 2017-07-22T02:23:45

See a solution process below:

First, we need to solve #x + 15 = 10# for #x#:

#x + 15 - color(red)(15) = 10 - color(red)(15)#

#x + 0 = -5#

#x = -5#

Now we need to substitute #-5# for each occurrence of #x# in the expression:

#x^3 - x^-2 + 16x^-1# becomes:

#(-5)^3 - (-5)^-2 + (16 * (-5)^-1) =>#

#-125 - (-5)^-2 + (16 * (-5)^-1) =>#

#-125 - 1/(-5)^2 + (16 * (-5)^-1) =>#

#-125 - 1/25 + (16 * (-5)^-1) =>#

#-125 - 1/25 + (16/(-5)^1) =>#

#-125 - 1/25 - 16/5 =>#

#-(25/25 xx 125) - 1/25 - (5/5 xx 16/5) =>#

#-3125/25 - 1/25 - 80/25 =>#

#-3206/25#