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+(−q) is the number located a distance |q| 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+(−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:

\[
p - q
\]

Here, \( p \) and \( q \) are both positive numbers.

Now, let's interpret \( p - q \):

- If \( p > q \), then \( p - q \) is positive, meaning the result is still a positive number, and it represents how far \( p \) is above \( q \).
- If \( p < q \), then \( p - q \) is negative, indicating that \( p \) is below \( q \) by a distance equal to \( q - p \).

The correct way to describe \( p + (-q) \) depends on the relationship between \( p \) and \( q \). However, none of the descriptions provided match the phrasing of this interpretation exactly.

But, since \( |p| \) and \( |q| \) denote the magnitudes (or absolute values) of \( p \) and \( q \) respectively, we consider the distance interpretations in the positive and negative directions.

The closest response from your options is:

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

This reflects the shift from \( q \) towards the left along the number line by the amount \( p \) or how \( p \) reduces \( q \) when subtracting \( q \) from \( p \). However, if \( p < q \), that interpretation might seem misleading because then you are moving further left off the number line from \( q \).

In conclusion, contextually and mathematically, \( p - q \) means you start at \( p \) and move towards negative \( q \), hence the best matching response is about nailing that distance difference as described.