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Example

Evaluating n+1n + 1 and n+1-n + 1 when n=5n = -5

Evaluate each expression by substituting 5-5 for nn and simplifying:

(a) n+1n + 1 when n=5n = -5: Replace nn with 5-5 to obtain 5+1-5 + 1. Adding a positive number to a negative number (different signs): the absolute values are 55 and 11, and 5>15 > 1, so take the sign of the larger absolute value (negative). Compute 51=45 - 1 = 4, so 5+1=4-5 + 1 = -4.

(b) n+1-n + 1 when n=5n = -5: Replace nn with 5-5 to obtain (5)+1-(-5) + 1. The expression (5)-(-5) means "the opposite of 5-5," which is 55. The expression becomes 5+1=65 + 1 = 6.

Notice that n+1n + 1 and n+1-n + 1 yield very different results (4-4 versus 66) for the same value of nn. This contrast reinforces that the notation n-n does not automatically represent a negative number — when nn itself is negative, n-n is positive.

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Updated 2026-04-21

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