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

Question

Avery Alexander · Accepted Answer

#x = 406/81#

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#

Last Response

Eli Assouline · Answer

undefined To solve the equation -(x-5)^(1/4) + 7/3 = 2, you can follow these steps:

1. Start by isolating the term with the radical. Subtract 7/3 from both sides of the equation:
   -(x-5)^(1/4) = 2 - 7/3

2. Simplify the right side of the equation:
   -(x-5)^(1/4) = 6/3 - 7/3
   -(x-5)^(1/4) = -1/3

3. To eliminate the negative sign, multiply both sides of the equation by -1:
   (x-5)^(1/4) = 1/3

4. Raise both sides of the equation to the fourth power to eliminate the fractional exponent:
   [(x-5)^(1/4)]^4 = (1/3)^4
   x - 5 = 1/81

5. Add 5 to both sides of the equation:
   x = 1/81 + 5

6. Simplify the right side of the equation:
   x = 1/81 + 405/81
   x = 406/81

7. Simplify the fraction:
   x = 406/81 = 5 1/81

Therefore, the solution to the equation -(x-5)^(1/4) + 7/3 = 2 is x = 5 1/81.