# Chapter 10 - Exponents and Radicals - 10.6 Solving Radical Equations - 10.6 Exercise Set - Page 668: 31

$x=\dfrac{80}{3}$

#### Work Step by Step

Using the properties of equality, the given equation, $\sqrt[4]{3x+1}-4=-1$, is equivalent to \begin{array}{l} \sqrt[4]{3x+1}=-1+4 \\\\ \sqrt[4]{3x+1}=3 .\end{array} Raising both sides to the $\text{ 4th }$ power, the solution to the equation above, $\sqrt[4]{3x+1}=3$, is \begin{array}{l} 3x+1=81 \\\\ 3x=81-1 \\\\ 3x=80 \\\\ x=\dfrac{80}{3} .\end{array} Upon checking, $x=\dfrac{80}{3}$ satisfies the given equation.

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