Solve the Inequality for y 5<2-3y<14

$5 < 2 - 3 y < 14$

Move all terms not containing $y$ from the center section of the inequality.

Subtract $2$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$5 - 2 < - 3 y < 14 - 2$

Subtract $2$ from $5$ .

$3 < - 3 y < 14 - 2$

Subtract $2$ from $14$ .

$3 < - 3 y < 12$

Divide each term in the inequality by $- 3$ .

$\frac{3}{- 3} > \frac{- 3 y}{- 3} > \frac{12}{- 3}$

Divide $3$ by $- 3$ .

$- 1 > \frac{- 3 y}{- 3} > \frac{12}{- 3}$

Cancel the common factor of $- 3$ .

Cancel the common factor.

$- 1 > \frac{- 3 y}{- 3} > \frac{12}{- 3}$

Divide $y$ by $1$ .

$- 1 > y > \frac{12}{- 3}$

Divide $12$ by $- 3$ .

$- 1 > y > - 4$

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$- 4 < y < - 1$

The result can be shown in multiple forms.

Inequality Form:

$- 4 < y < - 1$

Interval Notation:

$(- 4, - 1)$