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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 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 |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.

1 answer

To analyze the expression \( p + (-q) \), we can simplify it as follows:

  1. Since \( p \) and \( q \) are both positive numbers, \( -q \) represents a negative value.
  2. Therefore, \( p + (-q) \) simplifies to \( p - q \).

Now, we need to interpret what \( p - q \) means in relation to the number line:

  • If \( p > q \), then \( p - q \) is a positive number, indicating that the result is located at a distance of \( |p - q| \) from 0 towards the positive direction.
  • If \( p < q \), then \( p - q \) is a negative number, indicating that the result is located at a distance of \( |p - q| \) from 0 towards the negative direction.
  • If \( p = q \), then \( p - q = 0 \).

Since the question is specifically about the mechanics of the expression \( p + (-q) \), we want to find the phrasing that describes this operation correctly in relation to the distance from \( p \) and \( q \).

Among the given options, the one that correctly and completely describes the situation is:

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

This interpretation makes sense because when you subtract a positive \( q \) from \( p \), you are effectively moving \( q \) units left from \( p \) on the number line, which corresponds to moving in the negative direction.