\( \begin{array}{ll}\text { b) } 4 \sqrt{7 x+1}-2=14 & \text { c) } 2 \sqrt[4]{x-3}=4\end{array} \)

To solve the equation \( 4\sqrt{7x+1} - 2 = 14 \), start by isolating the square root. Add 2 to both sides, giving you \( 4\sqrt{7x+1} = 16 \). Next, divide by 4 to get \( \sqrt{7x+1} = 4 \). Square both sides to eliminate the square root, resulting in \( 7x + 1 = 16 \). Subtract 1, yielding \( 7x = 15 \), and finally divide by 7 to find \( x = \frac{15}{7} \). For the equation \( 2\sqrt[4]{x-3} = 4 \), start by isolating the fourth root. Divide both sides by 2, leading to \( \sqrt[4]{x-3} = 2 \). Raise both sides to the power of 4 to remove the fourth root, resulting in \( x - 3 = 16 \). Add 3 to both sides to find \( x = 19 \). These steps show how to deal with roots effectively in equations!