For the inequality x≤−3

Question

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

−7522
negative 75 over 22

−7–√
negative square root of 7

-10.1010
-10.1010

-2.101101110...
-2.101101110...

-3.14

Change the decimal to a fraction: 0.759(1 point)
Responses

7591000
759 over 1000

759999
759 over 999

75910
75 and 9 tenths

759100
7 and 59 over 100

Cannot be written as a fraction

Change the decimal to a fraction: 0.2626262626...(1 point)
Responses

2610
2 and 6 tenths

2626100
26 and 26 over 100

26100
26 over 100

Cannot be written as a fraction
Cannot be written as a fraction

26/99

Answer 1

Let's go through the questions one at a time.

For the inequality \( x \leq -3 \):

We need to check which of the listed numbers satisfy this inequality.

1. −75/22: \[ -\frac{75}{22} \approx -3.409 \quad (true) \]

2. −√7: \[ -\sqrt{7} \approx -2.645751311 \quad (false) \]

3. -10.1010: \[ -10.1010 \quad (true) \]

4. -2.101101110...: \[ -2.101101110... \quad (false) \]

5. -3.14: \[ -3.14 \quad (true) \]

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

• \(-75/22\)
• \(-10.1010\)
• \(-3.14\)

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Change the decimal to a fraction: \(0.759\)

To convert \(0.759\) to a fraction, we recognize it as: \[ \frac{759}{1000} \] So:

• 759/1000 is correct.

Change the decimal to a fraction: \(0.2626262626...\)

The repeating decimal \(0.262626...\) can be expressed as: \[ \frac{26}{99} \] So:

• 26/99 is correct.

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Summary of Answers:

1. For the inequality \( x \leq -3 \):

   • The true numbers are:
     • \(-75/22\)
     • \(-10.1010\)
     • \(-3.14\)

2. Change the decimal:

   • \(0.759\) → 759/1000
   • \(0.262626...\) → 26/99