Question:
Solve $3 x+8>2$, when
(i) x is an integer
(ii) x is a real number
Solution:
The given inequality is $3 x+8>2$.
$3 x+8>2$
$\Rightarrow 3 x+8-8>2-8$
$\Rightarrow 3 x>-6$
$\Rightarrow \frac{3 x}{3}>\frac{-6}{3}$
$\Rightarrow x>-2$
(i) The integers greater than $-2$ are $-1,0,1,2, \ldots$
Thus, when $x$ is an integer, the solutions of the given inequality are
$-1,0,1,2 \ldots$
Hence, in this case, the solution set is $\{-1,0,1,2, \ldots\}$.
(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 $(-2, \infty)$.