Let's solve the equation:

\[
x^3 - x^3 + x = 3
\]

### Step 1: Simplify the expression
Notice that \( x^3 - x^3 \) cancels out to zero. This simplifies the equation to:

\[
x = 3
\]

### Step 2: Conclusion
The solution to the equation is:

\[
x = 3
\]

Would you like more details or have any questions?

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Here are some related questions you might find interesting:
1. How do you solve more complex cubic equations like \( x^3 + 2x^2 - x = 5 \)?
2. How do you approach solving quadratic equations?
3. What are the properties of polynomials in terms of degree and roots?
4. How does the cancellation of terms affect the overall solution in algebraic equations?
5. How can you solve equations that involve fractions and exponents?

**Tip:** Always look for terms that cancel out early in the simplification process to avoid extra steps.

Discover how to simplify and solve the equation x³ - x³ + x = 3 with a detailed step-by-step guide. This problem focuses on basic algebraic simplification and solving linear equations, suitable for students in Grades 6-8.

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