https://file.aiquickdraw.com/mathbot/file/1736719782510hc56i72w.jpg

The inequality presented in the image is:

\[
\sqrt[3]{x + 7} \geq 3
\]

### Step-by-Step Solution:

1. **Eliminate the Cube Root**:
   To isolate \(x + 7\), cube both sides of the inequality:
   \[
   \left(\sqrt[3]{x + 7}\right)^3 \geq 3^3
   \]
   This simplifies to:
   \[
   x + 7 \geq 27
   \]

2. **Isolate \(x\)**:
   Subtract 7 from both sides:
   \[
   x \geq 27 - 7
   \]
   \[
   x \geq 20
   \]

### Final Solution:
The solution to the inequality is:
\[
x \geq 20
\]

---

Would you like further clarification or details? 

Here are 5 related questions for you to consider:
1. What are the properties of cube roots when solving inequalities?
2. How does cubing affect the direction of inequalities compared to squaring?
3. What would change if this were a square root instead of a cube root?
4. How do you verify solutions to inequalities like this one?
5. Can you explain how inequalities differ from equations when graphing?

**Tip**: When solving inequalities, always double-check whether the operation you apply (e.g., squaring, cubing) might reverse the inequality's direction.

Solve the inequality: cube root of (x + 7) ≥ 3.

Learn how to solve the cube root inequality √[3](x + 7) ≥ 3 step by step. This solution covers algebraic concepts such as cube root elimination and inequality solving, suitable for Grades 9-10.

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