Question

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

options:

-10.1010

-3.14

−√7

−75 over 22

-2.101101110...

Answer 1

To determine which numbers satisfy the inequality \( x \leq -3 \), we will check each of the provided values:

1. **-10.1010**: This number is less than -3, so it satisfies the inequality.
2. **-3.14**: This number is also less than -3, so it satisfies the inequality.
3. **−√7**: The value of \( \sqrt{7} \) is approximately 2.64575, making \( -\sqrt{7} \approx -2.64575 \), which is greater than -3. This does not satisfy the inequality.
4. **−75 over 22**: Calculating this value, \( -\frac{75}{22} \approx -3.409 \), which is less than -3. So it satisfies the inequality.
5. **-2.101101110...**: This number is greater than -3, so it does not satisfy the inequality.

Based on this evaluation, the numbers that satisfy the inequality \( x \leq -3 \) are:

- -10.1010
- -3.14
- −75 over 22