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.