Question

Solve: 3x+8 > 2, when

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

Answer 1

The given inequality is 3x+8 > 2.
3x-8 > 2
⇒ 3x-8-8 > 2-8
⇒ 3x > -6
⇒ $\frac {3x}{3}$ > $-\frac {6}{3}$
⇒ x > -2

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(i) The integers greater than –2 are –1, 0, 1, 2, …
Thus, when x is an integer, the solutions of the given inequality are –1, 0, 1, 2 …

Hence, in this case, the solution set is {–1, 0, 1, 2, …}.

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(ii) When x is a real number, the solutions of the given inequality are all the real numbers, which are greater than –2.

Thus, in this case, the solution set is (– 2, ∞).