Question

Solve the following inequation: $-3<x-2\le 9-2x$ , $xϵN$.

• A. $-1<x\le \frac{11}{3}$
  
• B. $-2<x\le \frac{11}{3}$
  
• C. $-1<x\le \frac{10}{3}$
  
• D. $1<x\le \frac{11}{3}$
  

Answer 1

The correct option is A

$-1<x\le \frac{11}{3}$

$-3<x-2\le 9-2x,xϵN\Rightarrow -3<x-2andx-2\le 9-2x\Rightarrow -x<-2+3and\Rightarrow x+2x\le 9+2\Rightarrow -x<1and\Rightarrow 3x\le 11\Rightarrow x>-1and\Rightarrow x\le \frac{11}{3}$
So, $-1<x\le \frac{11}{3}$