Question

Which of the following describes the sum p + (−q) where p
and q
are positive numbers??(1 point)
Responses

The sum p+(−q) is the number located a distance |p| from q in the negative direction.
The sum p plus left parenthesis negative q right parenthesis is the number located a distance Start Absolute Value p End Absolute Value from q in the negative direction.

The sum p+(−q) is the number located a distance |p| from q in the positive direction.
The sum negative p plus left parenthesis negative q right parenthesis is the number located a distance absolute value of p from q in the positive direction.

The sum p+(−q) is the number located a distance |q| from p in the positive direction.
The sum p plus left parenthesis negative q right parenthesis is the number located a distance Start Absolute Value q End Absolute Value from p in the positive direction.

D. The sum p+(−q) is the number located a distance |q| from p in the negative direction.

Answer 1

To analyze the expression \( p + (-q) \), we can rewrite it as \( p - q \).

Given that both \( p \) and \( q \) are positive numbers, the result of \( p - q \) will depend on the relative sizes of \( p \) and \( q \):

1. If \( p > q \), the result \( p - q \) will be positive.
2. If \( p < q \), the result \( p - q \) will be negative.
3. If \( p = q \), the result will be zero.

However, the question is specifically about the representation of \( p + (-q) \).

When we consider \( p + (-q) \):
- This expression can be interpreted as starting at \( p \) and moving \( q \) units in the negative direction.

Thus, the best option that describes this is:

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

Therefore, the correct answer is:

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