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Question
Find positive integers which are such that if 6 is subtracted from five times the integer then the resulting number cannot be greater than four times the integer.
Solution
Let the integer be x.
According to the given conditions,
⇒ 5x - 6 < 4x
⇒ 5x - 4x < 6
⇒ x < 6
Since x is positive, x can only have the values 1, 2, 3, 4, 5.
Solution set = {x : x < 6} = { 1, 2, 3, 4, 5}.
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