To solve the equation \(\sqrt[3]{2x - 1} = 2\), follow these steps:

1. **Cube both sides** to eliminate the cube root:

   \[
   (\sqrt[3]{2x - 1})^3 = 2^3
   \]

   Simplifying this gives:

   \[
   2x - 1 = 8
   \]

2. **Solve for \(x\)** by isolating \(x\):

   \[
   2x = 8 + 1
   \]

   \[
   2x = 9
   \]

   \[
   x = \frac{9}{2}
   \]

   \[
   x = 4.5
   \]

So, the solution is \(x = 4.5\).

Would you like further details or have any questions?

Here are some related questions you might find interesting:

1. How do you solve equations involving other roots, such as square roots or fourth roots?
2. What happens if the equation is \(\sqrt[3]{2x - 1} = -2\)?
3. How would you solve \(\sqrt[3]{2x + 3} = 4\)?
4. What is the general approach to solving equations with nested radicals?
5. Can you solve equations where the variables are inside both the base and the exponent, like \(x^{\frac{1}{3}} = 2\)?

**Tip:** When solving equations involving radicals, isolating the radical term first often simplifies the problem considerably.

Learn how to solve the cube root equation cbrt(2x - 1) = 2 with a detailed step-by-step solution. This problem involves cube roots and equation-solving techniques, suitable for students in Grades 8-10.

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