Given the following equation:
[tex]p\mleft(x+q\mright)^4=r[/tex]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":
[tex]\begin{gathered} \frac{p\mleft(x+q\mright)^4}{p}=\frac{r}{p} \\ \\ \mleft(x+q\mright)^4=\frac{r}{p} \end{gathered}[/tex]2. Remember that:
[tex]\sqrt[n]{a^n}=a[/tex]Then:
[tex]\begin{gathered} \sqrt[4]{(x+q)^4}=\sqrt[4]{\frac{r}{p}} \\ \\ x+q=\sqrt[4]{\frac{r}{p}} \end{gathered}[/tex]3. Now you have to apply the Subtraction property of equality by subtracting "q" from both sides of the equation:
[tex]\begin{gathered} x+q-(q)=\sqrt[4]{\frac{r}{p}}-(q) \\ \\ x=\sqrt[4]{\frac{r}{p}}-q \end{gathered}[/tex]The answer is:
[tex]x=\sqrt[4]{\frac{r}{p}}-q[/tex]