For the inequality x≤−3

Question

, 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.