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Question

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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 |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.

GPT-4o mini · Answer

Let's analyze the expression $ p + (-q) $. Given that $ p $ and $ q $ are positive numbers, the expression can be rewritten as: $$ p + (-q) = p - q $$ The sum $ p - q $ involves subtracting a positive number $ q $ from another positive number $ p $. There are two possible cases: 1. If $ p > q $, then $ p - q $ is positive, and the result is located a distance of $ q $ units to the left of $ p $ on a number line. 2. If $ p < q $, then $ p - q $ is negative, and the result is located a distance of $ q $ units in the negative direction from $ p $. Now, let's look at the options. Since the options seem to discuss distances, we'll focus on those that describe the position of $ p - q $: - The first option states: "The sum $ p + (-q) $ is the number located a distance $ |q| $ from $ p $ in the positive direction." - The second option states: "The sum $ p + (-q) $ is the number located a distance $ |p| $ from $ q $ in the positive direction." - The third option states: "The sum $ p + (-q) $ is the number located a distance $ |q| $ from $ p $ in the negative direction." - The fourth option states: "The sum $ p + (-q) $ is the number located a distance $ |p| $ from $ q $ in the negative direction." From our analysis, the most reasonable choice aligns with $ p - q $: - If $ p > q $: We are going $ q $ units to the left from $ p $. - If $ p < q $: We are $ |q| $ units away in the negative direction. Given the provided responses, the most accurate description of $ p + (-q) $ is: "The sum $ p + (-q) $ is the number located a distance $ |q| $ from $ p $ in the negative direction." So the correct response is the option that states: "The sum $ p + (-q) $ is the number located a distance $ |q| $ from $ p $ in the negative direction."