\( 3 \sqrt[3]{5 y+1}-2=-5 \) The solution set is

To solve the equation \( 3 \sqrt[3]{5y+1} - 2 = -5 \), let's first isolate the cube root. Adding 2 to both sides gives: \[ 3 \sqrt[3]{5y+1} = -3 \] Now, dividing by 3: \[ \sqrt[3]{5y+1} = -1 \] Next, we'll cube both sides: \[ 5y + 1 = (-1)^3 \] \[ 5y + 1 = -1 \] Subtracting 1 from both sides: \[ 5y = -2 \] Finally, dividing by 5: \[ y = -\frac{2}{5} \] So the solution set is \( \left\{ -\frac{2}{5} \right\} \). In conclusion, finding those hidden solutions often requires peeling back equations layer by layer, much like solving a mystery! Keep practicing and you’ll be a math detective in no time!