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 |q| from p in the negative 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 negative 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 |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.

Answer 1

To analyze the expression \( p + (-q) \), we can rewrite it as \( p - q \). Since \( p \) and \( q \) are both positive numbers, \( -q \) represents a negative value (specifically, it is the same as moving \( q \) units to the left of zero on the number line).

Thus, \( p - q \) indicates we start at \( p \) and subtract \( q \) from it, moving \( q \) units in the negative direction.

Given this reasoning, the correct description of the sum \( p + (-q) \) is:

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

This matches with the first response option.