Solve the Inequality for y -9<5-7y<=12

$- 9 < 5 - 7 y \leq 12$

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

Subtract $5$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 9 - 5 < - 7 y \leq 12 - 5$

Subtract $5$ from $- 9$ .

$- 14 < - 7 y \leq 12 - 5$

Subtract $5$ from $12$ .

$- 14 < - 7 y \leq 7$

Divide each term in the inequality by $- 7$ .

$\frac{- 14}{- 7} > \frac{- 7 y}{- 7} \geq \frac{7}{- 7}$

Divide $- 14$ by $- 7$ .

$2 > \frac{- 7 y}{- 7} \geq \frac{7}{- 7}$

Cancel the common factor of $- 7$ .

Cancel the common factor.

$2 > \frac{- 7 y}{- 7} \geq \frac{7}{- 7}$

Divide $y$ by $1$ .

$2 > y \geq \frac{7}{- 7}$

Divide $7$ by $- 7$ .

$2 > y \geq - 1$

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

$- 1 \leq y < 2$

The result can be shown in multiple forms.

Inequality Form:

$- 1 \leq y < 2$

Interval Notation:

$[- 1, 2)$