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The problem you've shared asks for the solution to the inequality:

\[
125 \geq 5^{2x + 2}
\]

### Step-by-step solution:

1. **Express 125 as a power of 5**:
   \[
   125 = 5^3
   \]
   Now, rewrite the inequality:
   \[
   5^3 \geq 5^{2x + 2}
   \]

2. **Since the bases are the same (both are powers of 5), we can compare the exponents**:
   \[
   3 \geq 2x + 2
   \]

3. **Solve for \( x \)**:
   Subtract 2 from both sides:
   \[
   3 - 2 \geq 2x
   \]
   Simplifying:
   \[
   1 \geq 2x
   \]
   Now, divide both sides by 2:
   \[
   \frac{1}{2} \geq x
   \]
   Or:
   \[
   x \leq \frac{1}{2}
   \]

### Solution Set:
The solution set is \( x \leq \frac{1}{2} \).

---

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

Here are 5 related questions:
1. How can you solve inequalities when the bases are different?
2. What happens if the base of the exponent is less than 1?
3. How do you graph the solution \( x \leq \frac{1}{2} \) on a number line?
4. How do you solve compound inequalities involving exponents?
5. Can you explain how to manipulate inequalities when the inequality sign is flipped?

**Tip:** Always check if you can express both sides of an inequality with a common base when working with exponential inequalities. This simplifies the problem greatly.

Find the value of x for the inequality: 125 ≥ 5^(2x + 2)

Learn how to solve the inequality 125 ≥ 5^(2x + 2) with a step-by-step solution. This problem involves algebraic concepts such as exponent comparison and solving inequalities. Suitable for students in Grades 8-10.

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