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The inequality for a number ( x ) decreased by two being at most four can be expressed as ( x - 2 \leq 4 ). The condition of being at least nine translates to ( x - 2 \geq 9 ). Therefore, the complete set of inequalities is ( x - 2 \leq 4 ) or ( x - 2 \geq 9 ). Simplifying these gives us ( x \leq 6 ) or ( x \geq 11 ).

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