To solve the equation:

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

Follow these steps:

### Step 1: Cube both sides to eliminate the cube root.
\[
\left(\sqrt[3]{2x - 1}\right)^3 = 1^3
\]
\[
2x - 1 = 1
\]

### Step 2: Add 1 to both sides to isolate \(2x\).
\[
2x = 1 + 1
\]
\[
2x = 2
\]

### Step 3: Divide both sides by 2 to solve for \(x\).
\[
x = \frac{2}{2} = 1
\]

### Final solution:
\[
x = 1
\]

Would you like a more detailed explanation or have any questions?

Here are 5 related questions for practice:
1. Solve \(\sqrt[3]{3x - 4} = 2\).
2. Solve \(\sqrt[3]{5x + 3} = 0\).
3. What is the cube root of 8?
4. If \(\sqrt[3]{x} = 5\), what is \(x\)?
5. Solve \(\sqrt[3]{x - 2} = -1\).

**Tip:** When dealing with cube roots, remember that cubing both sides eliminates the root, making the equation simpler to solve.

This detailed guide helps students solve the equation cbrt(2x - 1) = 1. It covers algebraic concepts such as cube roots and linear equations, walking through the steps to cube both sides, isolate the variable, and find the solution x = 1. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation