Question

for the inequality x less than or equal to -3, which number(s) listed makes the inequality true? Check ALL that apply

neg 75/22
-10.1010
neg square root of 7
-2.101101110
-3.14

Answer 1

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

1. **\(-\frac{75}{22}\)**:
- First, calculate \(-\frac{75}{22}\). This is approximately \(-3.409\), which is less than -3. **(True)**

2. **\(-10.1010\)**:
- \(-10.1010\) is less than -3. **(True)**

3. **\(-\sqrt{7}\)**:
- The value of \(-\sqrt{7}\) is approximately \(-2.645\), which is greater than -3. **(False)**

4. **\(-2.101101110\)**:
- \(-2.101101110\) is greater than -3. **(False)**

5. **\(-3.14\)**:
- \(-3.14\) is less than -3. **(True)**

Thus, the numbers that satisfy the inequality \( x \leq -3 \) are:
- \(-\frac{75}{22}\)
- \(-10.1010\)
- \(-3.14\)

So, the final answers are:
- **\(-\frac{75}{22}\)**
- **\(-10.1010\)**
- **\(-3.14\)**