Question

Solve $5x-3<7,$ when

(i) $x$ is an integer.

(ii) $x$ is a real number.

Answer 1

The given inequality is, $5x-3<7$
$\Rightarrow 5x-3+3<7+3$
$\Rightarrow 5x<10$
$\Rightarrow \frac{5x}{5}<\frac{10}{5}$
$\Rightarrow x<2$
(i) The integers less than 2 are $.......,-4,-3,-3,-1,0,1.$
Thus when $x$ is an integer, the solutions of the given inequality are
all the integral values of $x$ which are less than $2$.
(ii) When $x$ is real number the solution is given by $x<2$,
i.e., all real numbers $x$ which are less than 2.
Thus, the solution set of the given inequality is $x\in (-\infty ,2)$