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. Solution set = {-2, -1, 0, 1, 2, 3, 4, 5}

Answer 1

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

Given: $2y-3<y+1\le 4y+7$

$\Rightarrow 2y-3<y+1\text{and}y+1\le 4y+7$

Rule: If a term of an inequation is transferred from one side to the other side of the inequation, the sign of the term gets changed. Let's apply this rule in the above inequation.

$\Rightarrow 2y-y<3+1\text{and}1-7\le 4y-y$


$\Rightarrow y<4\text{and}-6\le 3y$

$\Rightarrow y<4andy\ge -2$

$\Rightarrow -2\le y<4$

Therefore, the solution set = {-2, -1, 0, 1, 2, 3}.