To solve for x in the equation

[tex] \sqrt[3]{2x - 3} = - 4[/tex]

we first cube both sides of the equation to get rid of the cube root:

[tex] 2x - 3 = (-4)^3[/tex]
[tex] 2x - 3 = -64[/tex]

Next, add 3 to both sides:

[tex] 2x = -64 + 3[/tex]
[tex] 2x = -61[/tex]

Divide by 2 to solve for x:

[tex] x = \frac{-61}{2}[/tex]

So, the solution to the equation is [tex] x = -\frac{61}{2}[/tex].