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.

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

1. If \( p > q \), then \( p - q \) will be positive.
2. If \( p = q \), then \( p - q = 0 \).
3. If \( p < q \), then \( p - q \) will be negative.

The statement that best describes the expression \( p + (-q) \) is:

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

This is because subtracting \( q \) from \( p \) can be conceptualized as starting at \( p \) and moving left (in the negative direction) towards zero by a distance of \( q \). If we visualize this on a number line, starting at \( p \) and moving \( q \) units to the left leads us to \( p - q \).