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

Question

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