How do you solve #9- root[ 3] { 3x - 5} = 7#?

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Answer 1 · 2017-07-08T12:03:14

#x=13/3 or 4.333333333#

#9-root3(3x-5)=7#

#:.-root3(3x-5)=7-9#

#:.-root3(3x-5)=-2#

multiply both sides by#-1#

#:.root3(3x-5)=2#

cube both sides

#:.(root3(3x-5))^3=(2)^3#

#:.root3a*root3a*root3a=a#

#:.3x-5=2^3#

#:.3x-5=8#

#:.3x=8+5#

#:.3x=13#

#:.color(blue)(x=13/3 or 4.333333333#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)(Check:#

substitute #color(blue)(x=4.333333333#

#:.9-root3(3(color(blue)4.333333333)-5)=7#

#:.9-root3(13-5)=7#

#:.-root3(13-5)=7-9#

#:.-root3(8)=-2#

Multiply both sides by #-1#

#:.root3(2*2*2)=2#

#:.root3(2)*root3(2)*root3(2)=2#

#:.color(blue)(2=2#