Question

Solve the following inequation: $-3<x-2\le 9-2x$ $xϵN$. Also, graph the solution set on the number line.
[4 MARKS]

Answer 1

Solving the inequation: 1 Mark each
Answer: 1 Mark
Solution on the number line: 1 Mark

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