Question

If y is an integer number then which of the following is true for $2y-3<y+1\le 4y+7$?

• A. Solution set = {-2,-1,0,1,2,3}
• B. Solution set = {-1,0,1,2,3,4}
• C. Solution set = {-2,-1,0,1,2,3,4}
• D. None

Answer 1

The correct option is A Solution set = {-2,-1,0,1,2,3}

$2y-3<y+1\le 4y+7$ $\Rightarrow 2y-3<y+1andy+1\le 4y+7$
$\Rightarrow y<4and-6\le 3y$
$\Rightarrow y<4andy\ge -2$
$\Rightarrow -2\le y<4$
Therefore, Solution set = {-2,-1,0,1,2,3}