Chapter 1 - Section 1.4 - Radical Equations; Equations Quadratic in Form; Factorable Equations - 1.4 Assess Your Understanding - Page 117: 13

$-13$

Add 3 on both sides of the equation to obtain: $\sqrt[3]{1-2x}-3+3=0+3 \\\sqrt[3]{1-2x}=3$ Cube both sides of the equation to obtain: $1-2x=3^3 \\1-2x=27$ Subtract 1 on both sides to obtain: $-2x = 26$ Divide -2 to both sides of the equation to obtain: $x=\frac{26}{-2} \\x=-13$ Thus, the solution is $\left\{-13\right\}$.