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

1 Answer
Barney V.
Jul 8, 2017

x=13/3 or 4.333333333

Explanation:

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

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