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For the inequality  x≤−3

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

-3.14
-3.14

-2.101101110...
-2.101101110...

−7522
negative 75 over 22

-10.1010
-10.1010

−7–√
negative square root of 7
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1 answer

To determine which of the numbers listed makes the inequality \( x \leq -3 \) true, we need to check if each number is less than or equal to -3.

  1. -3.14: This is less than -3. True.
  2. -2.101101110...: This is greater than -3. False.
  3. -7522: This is much less than -3. True.
  4. -10.1010: This is less than -3. True.
  5. −√7: The value of \(-\sqrt{7}\) is approximately -2.645751311, which is greater than -3. False.

Thus, the numbers that make the inequality \( x \leq -3 \) true are:

  • -3.14
  • -7522
  • -10.1010

So the correct responses are:

  • -3.14
  • −7522
  • -10.1010