If cbrt(2 - 3x) - cbrt(-x + 12) = 0, what is the value of x?

To solve the equation ( \sqrt[3]{2 - 3x} - \sqrt[3]{-x + 12} = 0 ), we can start by isolating one of the cube root terms. This leads us to the equation:

[

\sqrt[3]{2 - 3x} = \sqrt[3]{-x + 12}

]

Next, we cube both sides to eliminate the cube roots:

[

2 - 3x = -x + 12

]

Now, let's rearrange this equation to isolate (x). Begin by adding (3x) to both sides:

[

2 = 2x + 12

]

Then, subtract 12 from both sides:

[

2 - 12 = 2x

]

This simplifies to:

[

-10 = 2x

]

Next, divide both sides by 2:

[

x = -5

]

So, the solution to the equation is (x = -5). This is consistent with the calculations, thus confirming that this value satisfies the original equation.

By substituting ( x = -5 ) back into the original cube root