Question

Solve $3x+8>2,$ when (i) $x$ is an integer. (ii) $x$ is a real number

Answer 1

The given inequality is $3x+8>2$
$\Rightarrow 3x+8-8>2-8$
$\Rightarrow 3x>-6$
$\Rightarrow \frac{3x}{3}>\frac{-6}{3}$
$\Rightarrow x>-2$
(i) The integers greater than $-2$ are $-1,0,1,2,.......$
Thus when $x$ is an integer, the solutions of the given inequality are $-1,0,1,\mathrm{2............}$
(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 $(-2,\infty )$