Solve for z -14<2z-4<-2

$- 14 < 2 z - 4 < - 2$

Step 1

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

Add $4$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 14 + 4 < 2 z < - 2 + 4$

Add $- 14$ and $4$ .

$- 10 < 2 z < - 2 + 4$

Add $- 2$ and $4$ .

$- 10 < 2 z < 2$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 10}{2} < \frac{2 z}{2} < \frac{2}{2}$

Step 3

Divide $- 10$ by $2$ .

$- 5 < \frac{2 z}{2} < \frac{2}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- 5 < \frac{2 z}{2} < \frac{2}{2}$

Divide $z$ by $1$ .

$- 5 < z < \frac{2}{2}$

Step 5

Divide $2$ by $2$ .

$- 5 < z < 1$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 5 < z < 1$

Interval Notation:

$(- 5, 1)$

Step 7