What are the solutions to the inequality −10(2x+6)≤8(−5−2x)−6x
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The given inequality is 24x = 100
= x 100/24
= x 25/6
(i) It is evident that 1, 2, 3, and 4 are the only natural numbers less than 25/6
Thus, when x is a natural number, the solutions of the given inequality are 1, 2, 3, and 4.
Hence, in this case, the solution set is (1, 2, 3, 4)
(ii) The integers less than are ...–3, –2, –1, 0, 1, 2, 3, 4.
Thus, when x is an integer, the solutions of the given inequality are ...–3, –2, –1, 0, 1, 2, 3, 4.
Hence
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