https://file.aiquickdraw.com/mathbot/file/1726181551884461guwnq.jpg

To determine which inequality is true when \( x = -12 \), let's evaluate each inequality by substituting \( x = -12 \) into each option.

### Option A: 
\[
0.75x + 22 < 20
\]
Substitute \( x = -12 \):
\[
0.75(-12) + 22 < 20
\]
\[
-9 + 22 < 20
\]
\[
13 < 20 \quad \text{(True)}
\]

### Option B:
\[
15 - \frac{1}{2}x > 21
\]
Substitute \( x = -12 \):
\[
15 - \frac{1}{2}(-12) > 21
\]
\[
15 + 6 > 21
\]
\[
21 > 21 \quad \text{(False)}
\]

### Option C:
\[
11 - 2x \leq 17
\]
Substitute \( x = -12 \):
\[
11 - 2(-12) \leq 17
\]
\[
11 + 24 \leq 17
\]
\[
35 \leq 17 \quad \text{(False)}
\]

### Option D:
\[
3.5x - 19 \geq -60
\]
Substitute \( x = -12 \):
\[
3.5(-12) - 19 \geq -60
\]
\[
-42 - 19 \geq -60
\]
\[
-61 \geq -60 \quad \text{(False)}
\]

### Conclusion:
The correct answer is **A**: \( 0.75x + 22 < 20 \) is true when \( x = -12 \).

Would you like further explanation on any step?

### Related Questions:
1. What would happen if \( x = -10 \) in the inequality \( 0.75x + 22 < 20 \)?
2. How can you solve inequalities like \( 15 - \frac{1}{2}x > 21 \) for different values of \( x \)?
3. What are the steps to graph the inequality \( 3.5x - 19 \geq -60 \)?
4. How can you rewrite \( 11 - 2x \leq 17 \) as an equality?
5. Why do inequalities flip the sign when multiplying by negative numbers?

**Tip:** Always double-check inequalities by substituting values to confirm if they hold true.

Which inequality is true when the value of x is -12?

Learn how to determine which inequality is true when x equals -12. This problem involves substituting x into four different inequalities and simplifying to find the correct answer. Suitable for students in Grades 7-9.

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