https://file.aiquickdraw.com/mathbot/file/17263122807393gwq9n0e.jpg

The inequality in the image is:

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

### Step-by-Step Solution:

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

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

3. **Solve for \( x \):**
   \[
   3 - 2 \geq 2x
   \]
   \[
   1 \geq 2x
   \]
   \[
   \frac{1}{2} \geq x
   \]
   This can also be written as:
   \[
   x \leq \frac{1}{2}
   \]

### Solution Set:
\[
x \leq \frac{1}{2}
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you solve exponential inequalities in general?
2. What are the rules for comparing exponents when the bases are equal?
3. How do you express logarithmic inequalities from this exponential inequality?
4. Can this inequality be solved using logarithms instead of exponent rules?
5. What is the graph of the solution set \( x \leq \frac{1}{2} \)?

**Tip:** When solving exponential equations or inequalities, always try to express terms with the same base to simplify the comparison of exponents.

Find the value of x for the inequality 125 ≥ 5^(2x+2) and show the solution set.

Learn how to solve the exponential inequality 125 ≥ 5^(2x+2) with a detailed step-by-step solution. This problem covers key algebraic concepts such as exponents and exponential inequalities. Suitable for students in Grades 9-12.

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