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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 |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 |q| from p in the positive direction.

3 answers

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

Given that \( p \) and \( q \) are positive numbers, \( -q \) represents a negative value. Therefore, when you add \( p \) and \( -q \), you are effectively subtracting \( q \) from \( p \).

The expression can be interpreted as follows:

  1. \( p + (-q) = p - q \).
  2. Since \( p \) and \( q \) are positive, the result will depend on the relative sizes of \( p \) and \( q \):
    • If \( p > q \), the result will be positive.
    • If \( p < q \), the result will be negative.

In terms of distance on a number line:

  • The sum \( p + (-q) \) or \( p - q \) is located at a distance \( |q| \) from \( p \), moving in the negative direction if \( q \) is being subtracted.

Thus, the correct description is:

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

are you correct?

Let's break down the expression \( p + (-q) \) carefully.

  1. \( p \) and \( q \) are both positive numbers.
  2. The term \( -q \) means you are subtracting \( q \) from \( p \). So, \( p + (-q) = p - q \).

Analyzing the Expression \( p - q \)

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

Distance on the Number Line

  • The result \( p - q \) can be thought of in terms of its position relative to \( p \):
    • If \( p > q \): The expression \( p - q \) lies to the left of \( p \) on the number line by a distance \( q \).
    • If \( p < q \): The expression is a negative number and doesn't lie to the left of \( p \) since we start from a positive value \( p \).

Conclusion

The correct representation of the situation, focusing on the distance, would be:

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

This matches a statement from your original list. Sorry for any confusion, but the explanation above confirms that this choice accurately describes \( p + (-q) \). If you're looking for a specific option from your list that captures this idea, you would select:

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