Question

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

Answer 1

`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