Question

Solve the following linear inequations in R.

Solve : 4x-2<8, when

(i) $xϵR$ (ii) $xϵZ$ (iii) $xϵN$

Answer 1

Now,

4x-2 <8

$\Rightarrow 4x<8+2\Rightarrow 4x<10\Rightarrow x<\frac{10}{4}=\frac{5}{2}\left(i\right)IfxϵR,thenx<\frac{5}{2}\Rightarrow xϵ(-\infty ,-\frac{5}{2})\left(ii\right)IfxϵZthenx<\frac{5}{2}\Rightarrow xϵ\{...,-2,-1,0,1,2\}\left(iii\right)ifxϵNthenx<\frac{5}{2}\Rightarrow xϵ\{1,2\}$