Question

Solve $5x-3<3x+1$ when
(i) $x$ is an integer (ii) $x$ is a real number

Answer 1

We have $5x-3<3x+1$
$\Rightarrow 5x-3+3<3x+1+3$
$\Rightarrow 5x<3x+4$
$\Rightarrow 5x-3\times <3x+4-3x$
$\Rightarrow 2x<4\Rightarrow x<2$
(i) When x is an integer the solutions of the given inequality are $\{.............,-4,-3,-2,-1,0,1\}$
(ii) When x is a real number the solutions of the inequality are given by x < 2 i.e. all real number x which are less than 2 Therefore the solution set of the inequality is $x\in (-\infty ,2)$