Chapter 1 - 1.6 - Other Types of Equations - 1.6 Exercises - Page 128: 35

$x=-\frac{55}{2}$

$4+\sqrt[3] {2x-9}=0$ $\sqrt[3] {2x-9}=-4~~$ (Cube both sides) $(\sqrt[3] {2x-9})^3=(-4)^3$ $2x-9=-64$ $2x=-64+9=-55$ $x=-\frac{55}{2}$ Check the solution: $4+\sqrt[3] {2(-\frac{55}{2})-9}=4+\sqrt[3] {2(-55-9})=4+\sqrt[3] {-64}=4+\sqrt[3] {(-4)^3}=4-4=0$