Given the following equation:

You can solve for the variable "x" as following:
1. You need to apply the Division property of equality by dividing both sides of the equation by "p":

2. Remember that:
![\sqrt[n]{a^n}=a](https://img.qammunity.org/2023/formulas/mathematics/college/iip6mtffd1c87x2h11rrrir6hfqw2jfavg.png)
Then:
![\begin{gathered} \sqrt[4]{(x+q)^4}=\sqrt[4]{(r)/(p)} \\ \\ x+q=\sqrt[4]{(r)/(p)} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/8cps1i5x4h73r6kkvg74qinnk2kco6v0bz.png)
3. Now you have to apply the Subtraction property of equality by subtracting "q" from both sides of the equation:
![\begin{gathered} x+q-(q)=\sqrt[4]{(r)/(p)}-(q) \\ \\ x=\sqrt[4]{(r)/(p)}-q \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/m13395f9cmsfcfrtgmpz4wd8k63yakk9qr.png)
The answer is:
![x=\sqrt[4]{(r)/(p)}-q](https://img.qammunity.org/2023/formulas/mathematics/college/eg416o7dwp9g50j2oe1ufd62u670g72rgy.png)