Question

Which of the following describes the sum p + (-9) where p and q are positive
numbers?? (1 point)
The sum p+(-q) is the number located a distance |p| from q in the negative
direction.
The sum p+(-q) is the number located a distance |g| from p in the positive
direction.
The sum p+(-9) is the number located a distance | 9| from p in the negative
direction.
The sum p+(-9) is the number located a distance |p| from q in the positive
direction.

Answer 1

To analyze the sum \( p + (-9) \), we recognize that it can be rewritten as \( p - 9 \).

We can consider what this means in terms of distance on the number line:
- \( p \) is a positive number.
- \( -9 \) indicates that we are moving 9 units in the negative direction from \( p \).

Therefore, the sum \( p + (-9) \) results in a value that is \( p \) minus 9. This represents a movement away from \( p \) in the negative direction by a distance of 9.

Now, let's evaluate the provided statements:

1. **The sum \( p+(-q) \) is the number located a distance \(|p|\) from \( q \) in the negative direction.**
- This is inaccurate since it discusses \( p+(-q) \) rather than \( p + (-9) \).

2. **The sum \( p+(-q) \) is the number located a distance \(|g|\) from \( p \) in the positive direction.**
- This is also incorrect because it discusses \( p + (-q) \) instead of \( p + (-9) \).

3. **The sum \( p+(-9) \) is the number located a distance \(|9|\) from \( p \) in the negative direction.**
- This statement is accurate. Moving from \( p \) by a distance of 9 in the negative direction indeed gives us \( p - 9 \).

4. **The sum \( p+(-9) \) is the number located a distance \(|p|\) from \( q \) in the positive direction.**
- This statement does not apply here as it misrepresents the relationship between \( p \) and \( -9 \).

Thus, the correct description of \( p + (-9) \) is:

**"The sum \( p+(-9) \) is the number located a distance |9| from \( p \) in the negative direction."**