How do you solve #\root[ 3] { 8x - 6} = \root [ 3] { 9x + 5}#?

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Answer 1 · 2017-07-15T15:37:14

See a solution process below:

First, cube each side of the equation to eliminate the radicals while keeping the equation balanced:

#(root(3)(8x - 6))^3 = (root(3)(9x + 5))^3#

#8x - 6 = 9x + 5#

Now, subtract #color(red)(8x)# and #color(blue)(5)# from each side of the equation to solve for #x# while keeping the equation balanced:

#-color(red)(8x) + 8x - 6 - color(blue)(5) = -color(red)(8x) + 9x + 5 - color(blue)(5)#

#0 - 11 = (-color(red)(8) + 9)x + 0#

#-11 = 1x#

#-11 = x#

#x = -11#