Question

List the elements of the solution set of the inequation $-3<x-2\le 9-2x;x\in N$

• A. { 0, 1, 2, 3 }
• B. { 1, 2, 3 }
• C. { -1, 0, 1, 2, 3 }
• D. { -1, 0, 1, 2 }

Answer 1

The correct option is B { 1, 2, 3 }

Given: $-3<x-2\le 9-2x$

$\Rightarrow -3<x-2\text{and}x-2\le 9-2x$

$\Rightarrow -3+2<x\text{and}x+2x\le 9+2$

$\Rightarrow x>-1\text{and}3x\le 11$

$\Rightarrow x>-1\text{and}x\le 11/3$

Since x $\in$ N,

Elements of solution set are { 1, 2, 3 }.