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The problem shown is asking to find the equivalent inequality for \( y^2 \geq 9 \).

### Step-by-Step Solution:

1. **Start with the given inequality**:
   \[
   y^2 \geq 9
   \]

2. **Take the square root of both sides**:
   \[
   y \geq 3 \quad \text{or} \quad y \leq -3
   \]
   This is because when you take the square root of both sides of an equation involving a squared term, you get both the positive and negative roots.

   This means that the values of \( y \) must either be greater than or equal to 3 or less than or equal to -3.

3. **Conclusion**:
   The solution to this inequality can be expressed as:
   \[
   y \geq 3 \quad \text{or} \quad y \leq -3
   \]

Thus, the correct answer is **option E**: \( y \leq -3 \) or \( y \geq 3 \).

Let me know if you need further explanation or details!

Here are 5 related questions for further understanding:
1. What are the steps to solving inequalities involving squared terms?
2. How do absolute values relate to squared inequalities like \( y^2 \geq 9 \)?
3. What happens when we deal with inequalities involving higher powers, like cubes?
4. How can we solve compound inequalities involving "and" and "or"?
5. How do graphical representations of quadratic inequalities look?

**Tip**: Always remember to check both the positive and negative roots when solving squared inequalities!

The inequality y^2 ≥ 9 is equivalent to?

Understand how to solve the quadratic inequality y^2 ≥ 9 through step-by-step instructions. This problem helps students grasp concepts such as inequalities involving squared terms and their solutions. Suitable for middle and high school students.

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