Question

Solve $5x-3<7$ when

(i) Solve $5x-3<7$ when
$x$ is an integer

(ii)Solve $5x-3<7$ when
$x$ is a real number

Answer 1

(i) $x$ is an integer

Given : $5x-3<7$
$\Rightarrow 5x<7+3$
$\Rightarrow x<\frac{10}{5}$
$\Rightarrow x<2$
Since $x$ is an integer. i.e, $x$ can be $...,-3,-2,-1,0,1,2,...$

We need to find values of $x$ which is less than $2$.
i.e., $x$ can be $...,-3,-2,-1,0,1=\{....,-3,-2,-1,0,1\}$

(ii) $x$ is a real number
Given : $5x-3<7$
$\Rightarrow x<7+3$
$\Rightarrow x<\frac{10}{5}$
$\Rightarrow x<2$
Since $x$ is a real number which is less than $2$.
Thus, $x\in (-\infty ,2)$