Solve the Inequality for z -36<3z-6<-15

$- 36 < 3 z - 6 < - 15$

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

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

$- 36 + 6 < 3 z < - 15 + 6$

Add $- 36$ and $6$ .

$- 30 < 3 z < - 15 + 6$

Add $- 15$ and $6$ .

$- 30 < 3 z < - 9$

Divide each term in the inequality by $3$ .

$\frac{- 30}{3} < \frac{3 z}{3} < \frac{- 9}{3}$

Divide $- 30$ by $3$ .

$- 10 < \frac{3 z}{3} < \frac{- 9}{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$- 10 < \frac{3 z}{3} < \frac{- 9}{3}$

Divide $z$ by $1$ .

$- 10 < z < \frac{- 9}{3}$

Divide $- 9$ by $3$ .

$- 10 < z < - 3$

The result can be shown in multiple forms.

Inequality Form:

$- 10 < z < - 3$

Interval Notation:

$(- 10, - 3)$