Question

For the inequality x≤−3
, which number(s) listed makes the inequality true? (Check ALL that apply!)(3 points)
Responses

-3.14
-3.14

−75/22
negative 75 over 22

-10.1010
-10.1010

−7–√
negative square root of 7

-2.101101110...

Answer 1

To determine which numbers make the inequality \( x \leq -3 \) true, we need to check each option to see if it meets this condition.

1. **-3.14**: This number is less than -3 (specifically, -3.14 is smaller), so it satisfies the inequality. **(True)**

2. **−75/22**: Calculating this gives approximately -3.409 (since \(-75 ÷ 22 \approx -3.409\)), which is also less than -3. Thus, it satisfies the inequality. **(True)**

3. **-10.1010**: This number is also less than -3. Therefore, it satisfies the inequality. **(True)**

4. **−7–√** (which refers to \(-\sqrt{7}\)): The square root of 7 is approximately 2.645, thus \(-\sqrt{7}\) is approximately -2.645, which is greater than -3. Therefore, it does not satisfy the inequality. **(False)**

5. **-2.101101110...**: This number is greater than -3. Thus, it does not satisfy the inequality. **(False)**

### Summary of responses:
- **-3.14:** True
- **−75/22:** True
- **-10.1010:** True
- **−7–√:** False
- **-2.101101110...:** False

The correct answers are **-3.14**, **−75/22**, and **-10.1010**.