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Question
Solve the given inequality for real x: x + `x/2` + `x/3` < 11
Solution
`x + x/2` + `x/3` <11`
= `x(1 + 1/2 + 1/3) < 11`
= `(6x + 3x + 2x)/6 < 11`
= `(11x)/6 < 11`
= `(11x)/(6 xx 11) < 11/11`
= `x/6 < 1`
= x < 6
Thus, all real numbers x, which are less than 6, are the solutions of the given inequality.
Hence, the solution set of the given inequality is (–∞, 6).
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