Solve for z -11<-2z-1<7

$- 11 < - 2 z - 1 < 7$

Step 1

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

Add $1$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 11 + 1 < - 2 z < 7 + 1$

Add $- 11$ and $1$ .

$- 10 < - 2 z < 7 + 1$

Add $7$ and $1$ .

$- 10 < - 2 z < 8$

Step 2

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

$\frac{- 10}{- 2} > \frac{- 2 z}{- 2} > \frac{8}{- 2}$

Step 3

Divide $- 10$ by $- 2$ .

$5 > \frac{- 2 z}{- 2} > \frac{8}{- 2}$

Step 4

Cancel the common factor of $- 2$ .

Cancel the common factor.

$5 > \frac{- 2 z}{- 2} > \frac{8}{- 2}$

Divide $z$ by $1$ .

$5 > z > \frac{8}{- 2}$

Step 5

Divide $8$ by $- 2$ .

$5 > z > - 4$

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.

$- 4 < z < 5$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 4 < z < 5$

Interval Notation:

$(- 4, 5)$

Step 8