Question

Which statements describe the solutions to the inequality x less-than negative 20? Check all that apply.
There are infinite solutions.
Each solution is negative.
Each solution is positive.
The solutions are both positive and negative.
The solutions contain only integer values.
The solutions contain rational number values.

Answer 1

To analyze the inequality \( x < -20 \), let's consider the statements one by one:

1. **There are infinite solutions.**
- **True.** There are infinitely many values of \( x \) that are less than -20 (for example, -21, -22, -100, etc.).

2. **Each solution is negative.**
- **True.** Every solution \( x \) must be less than -20, which means all solutions are negative.

3. **Each solution is positive.**
- **False.** Since \( x \) must be less than -20, no solutions can be positive.

4. **The solutions are both positive and negative.**
- **False.** All solutions are negative, so the set cannot include positive values.

5. **The solutions contain only integer values.**
- **False.** While there are integer solutions, the inequality also includes non-integer values (e.g., -20.5, -21.3, etc.).

6. **The solutions contain rational number values.**
- **True.** The inequality allows for any rational number (including fractions) that is less than -20.

In summary, the correct statements are:

- There are infinite solutions.
- Each solution is negative.
- The solutions contain rational number values.