Solve for y 2<6-2y<5

$2 < 6 - 2 y < 5$

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

Subtract $6$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$2 - 6 < - 2 y < 5 - 6$

Subtract $6$ from $2$ .

$- 4 < - 2 y < 5 - 6$

Subtract $6$ from $5$ .

$- 4 < - 2 y < - 1$

Divide each term in the inequality by $- 2$ .

$\frac{- 4}{- 2} > \frac{- 2 y}{- 2} > \frac{- 1}{- 2}$

Divide $- 4$ by $- 2$ .

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

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Dividing two negative values results in a positive value.

$2 > y > \frac{1}{2}$

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

$\frac{1}{2} < y < 2$

The result can be shown in multiple forms.

Inequality Form:

$\frac{1}{2} < y < 2$

Interval Notation:

$(\frac{1}{2}, 2)$