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 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 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 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 |p| from q in the negative direction.

Answer 1

To analyze the expression \( p + (-q) \):

1. Since \( q \) is a positive number, \( -q \) is a negative number.
2. The expression \( p + (-q) \) can be rewritten as \( p - q \).

Now, let's consider the implications of this expression:

• If \( p > q \), then \( p - q \) is positive.
• If \( p < q \), then \( p - q \) is negative.
• If \( p = q \), then \( p - q = 0\).

The interpretation regarding “distances” involves understanding how the value of \( p - q \) relates to the number line:

• If we think of \( p \) as a point on the number line representing the positive quantity \( p \) and \( -q \) as moving in the negative direction by \( q \), then \( p + (-q) = p - q \) results in a value that is located at a distance of \( |q| \) from \( p \) in the negative direction when \( p < q \).

Considering your choices, the appropriate description among them would be:

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

So the right response is that one.