Question:
Solve each of the following in equations and represent the solution set on the number line.
$3 x+8>2$, where (i) $x \in Z$, (ii) $x \in R$.
Solution:
(i) $3 x+8>2, x \in Z$
Subtracting 8 from both the sides in above equation
$3 x+8-8>2-8$
$3 x>-6$
Dividing both the sides by 3 in above equation
$\frac{3 x}{3}>\frac{-6}{3}$
Thus, $x>-2$
Since x is an integer
Therefore, possible values of x can be
$x=\{-1,0,1,2,3, \ldots\}$
(ii) $3 x+8>2, x \in R$
Subtracting 8 from both the sides in above equation
$3 x+8-8>2-8$
$3 x>-6$
Dividing both the sides by 3 in above equation
$\frac{3 x}{3}>\frac{-6}{3}$
Thus, $x>-2$
$x \in(-2, \infty)$
