How do you solve #-(x-5)^(1/4)+7/3=2#?

1 Answer
John D.
May 24, 2017

#x = 406/81#

Explanation:

Subtract #7/3# from both sides.

#-(x-5)^(1/4)+7/3-color(red)(7/3)=2-color(red)(7/3)#

#color(white)"XXXXX-."-(x-5)^(1/4) = -1/3#

Now multiply both sides by #-1#.

#color(blue)(-1)(-(x-5)^(1/4))=color(blue)(-1)(-1/3)#

#color(white)"XXXXX"(x-5)^(1/4) = 1/3#

Next, take both sides to the power of #4#.

#color(orange)((color(black)((x-5))^color(black)(1/4)))^color(orange)4 = color(orange)((color(black)(1/3)))^color(orange)4#

#(x-5) = 1/81#

Finally, add #5# to both sides.

#x-5+color(limegreen)5=1/81+color(limegreen)5#

#x = 406/81#

Final Answer

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