Which of the following describes the sump + (-9) where p and q are positive numbers?? (1 point)

Question

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

Answer 1

To analyze the expression \( p + (-q) \), we can rewrite it as \( p - q \). This means we are subtracting the positive number \( q \) from the positive number \( p \).

Now, let's interpret this geometrically:

• If \( p \) is greater than \( q \), then \( p - q \) is a positive number, and it is located a distance \( q \) from \( p \) in the negative direction (moving left on the number line).
• If \( p \) is less than \( q \), then \( p - q \) is a negative number, and it represents moving \( q \) units to the left of \( p \).

Given this understanding, the correct description from the options provided is:

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