Question

For the inequality x≤−3
, 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:
- \(-75/22\)
- \(-10.1010\)
- \(-3.14\)

---

### 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.

---

### 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**