Question

Solve: 5x - 3 < 7, when

1. x is an integer.
2. x is a real number.

Answer 1

The given inequality is 5x-3 < 7.
5x-3 < 7
⇒ 5x-3+3 < 7+3
⇒ 5x < 10
⇒ $\frac {5x}{5}$ < $\frac {10}{5}$
⇒ x< 2

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(i) The integers less than 2 are …, –4, –3, –2, –1, 0, 1.
Thus, when x is an integer, the solutions of the given inequality are …, –4, –3, –2, –1, 0, 1.
Hence, in this case, the solution set is {…, –4, –3, –2, –1, 0, 1}.

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(ii) When x is a real number, the solutions of the given inequality are given by x < 2, that is, all real numbers x which are less than 2.
Thus, the solution set of the given inequality is x (–∞, 2).