Question:
Solve each of the following in equations and represent the solution set on the number line.
$-2 x>5$, where (i) $x \in Z$, (ii) $x \in R$.
Solution:
(i) $-2 x>5, x \in Z$
Multiply both the sides by -1 in above equation,
$-2 x(-1)>5(-1)$
$2 x<-5$
Dividing both the sides by 2 in above equation,
$\frac{2 x}{2}<\frac{-5}{2}$
$x<\frac{-5}{2}$
$x<2.5$
Since, x is an integer
Therefore, possible values of x can be
$x=\{\ldots,-2,-1,0,1,2\}$
(ii) $-2 x>5, x \in R$
Multiply both the sides by -1 in above equation,
$-2 x(-1)>5(-1)$
$2 x<-5$
Dividing both the sides by 2 in above equation,
$\frac{2 x}{2}<\frac{-5}{2}$
$x<\frac{-5}{2}$
Therefore,
$x \in\left(-\infty, \frac{-5}{2}\right)$
