Solve for y 3x<2y+2<12

$3 x < 2 y + 2 < 12$

Step 1

Solve $3 x < 2 y + 2$ for $y$ .

Rewrite so $y$ is on the left side of the inequality.

$2 y + 2 > 3 x$

Subtract $2$ from both sides of the inequality.

$2 y > 3 x - 2$

Divide each term in $2 y > 3 x - 2$ by $2$ and simplify.

Divide each term in $2 y > 3 x - 2$ by $2$ .

$\frac{2 y}{2} > \frac{3 x}{2} + \frac{- 2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} > \frac{3 x}{2} + \frac{- 2}{2}$

Divide $y$ by $1$ .

$y > \frac{3 x}{2} + \frac{- 2}{2}$

Simplify the right side.

Divide $- 2$ by $2$ .

$y > \frac{3 x}{2} - 1$

Step 2

Solve $2 y + 2 < 12$ for $y$ .

Move all terms not containing $y$ to the right side of the inequality.

Subtract $2$ from both sides of the inequality.

$2 y < 12 - 2$

Subtract $2$ from $12$ .

$2 y < 10$

Divide each term in $2 y < 10$ by $2$ and simplify.

Divide each term in $2 y < 10$ by $2$ .

$\frac{2 y}{2} < \frac{10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} < \frac{10}{2}$

Divide $y$ by $1$ .

$y < \frac{10}{2}$

Simplify the right side.

Divide $10$ by $2$ .

$y < 5$

Step 3

Find the intersection of $y > \frac{3 x}{2} - 1$ and $y < 5$ .

$\frac{3 x}{2} - 1 < y < 5$

Step 4