Solve for z -10<-2z-2<12

$- 10 < - 2 z - 2 < 12$

Step 1

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

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

$- 10 + 2 < - 2 z < 12 + 2$

Add $- 10$ and $2$ .

$- 8 < - 2 z < 12 + 2$

Add $12$ and $2$ .

$- 8 < - 2 z < 14$

Step 2

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

$\frac{- 8}{- 2} > \frac{- 2 z}{- 2} > \frac{14}{- 2}$

Step 3

Divide $- 8$ by $- 2$ .

$4 > \frac{- 2 z}{- 2} > \frac{14}{- 2}$

Step 4

Cancel the common factor of $- 2$ .

Cancel the common factor.

$4 > \frac{- 2 z}{- 2} > \frac{14}{- 2}$

Divide $z$ by $1$ .

$4 > z > \frac{14}{- 2}$

Step 5

Divide $14$ by $- 2$ .

$4 > z > - 7$

Step 6

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

$- 7 < z < 4$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 7 < z < 4$

Interval Notation:

$(- 7, 4)$

Step 8