To find the sum \( p + q \) when \( p \) is positive and \( q \) is negative, we need to start from point \( p \) and move left on the number line by the absolute value of \( q \) (since \( q \) is negative).
Let's analyze the descriptions of the number lines you provided:
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First image: Shows \( p \) at 5 intervals to the right of 0. A leftward arrow labeled \( |q| \) (the absolute value of \( q \)) starts at \( p \) and ends 4 intervals to the left of \( p \). This is correct because it indicates moving left from \( p \) by the positive distance \( |q| = 4 \), representing the addition of a negative number to a positive one.
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Second image: Begins at \( p \) and incorrectly moves right by \( |q| \) (which would imply adding a positive number instead of subtracting). This does not reflect the operation of adding a negative.
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Third image: Shows \( p \) at the seventh interval from the left, with zero marked at 2 intervals to the right of \( p \). An arrow moves left to the second interval from the left, indicating that \( q \) has a value that brings us back by the absolute value of \( q \). This method reflects the correct representation of adding a negative number.
Based on these descriptions, the correct number line for the operation \( p + q \) is displayed in the first image, as it correctly illustrates moving left from \( p \) to find the sum.