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:
-
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 \( p + (-9) \).
-
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 \( p + (-9) \).
-
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 \( p - 9 \).
-
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."