Question:
Solve each of the following in equations and represent the solution set on the number line.
$5 x+2<17$, where (i) $x \in Z$, (ii) $x \in R$.
Solution:
(i) $5 x+2<17, x \in Z$
Subtracting 2 from both the sides in the above equation,
$5 x+2-2<17-2$
$5 x<15$
Dividing both the sides by 5 in the above equation,
$\frac{5 x}{5}<\frac{15}{5}$
$x<3$
Since x is an integer
Therefore, possible values of x can be
$x=\{\ldots,-2,-1,0,1,2\}$
(ii) $5 x+2<17, x \in R$
Subtracting 2 from both the sides in above equation
$5 x+2-2<17-2$
$5 x<15$
Dividing both the sides by 5 in above equation
$\frac{5 x}{5}<\frac{15}{5}$
$x<3$
Therefore, $x \in(-\infty, 3)$
