To determine which inequality symbol produces an inequality with an infinite number of nonsolutions, let's analyze each of the three symbols you've given:
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Greater than (>): The inequality \( x > a \) has an infinite number of solutions (all values greater than \( a \)). The nonsolutions would be all values less than or equal to \( a \), which is also infinite.
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Less than (<): The inequality \( x < a \) also has an infinite number of solutions (all values less than \( a \)). The nonsolutions would be all values greater than or equal to \( a \), which is again infinite.
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Not equal to (≠): The inequality \( x \neq a \) has all values except \( a \) as solutions, which is still infinite (since there are infinitely many values other than \( a \)). However, the only nonsolution is the single value \( a \), which is a finite set and not infinite.
From this analysis, the symbol that produces an inequality with an infinite number of nonsolutions is the not equal to (≠) symbol. It has infinite solutions but only one nonsolution, which is \( a \) itself.