Solve for z -9<-2z+1<-5

$- 9 < - 2 z + 1 < - 5$

Step 1

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

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

$- 9 - 1 < - 2 z < - 5 - 1$

Subtract $1$ from $- 9$ .

$- 10 < - 2 z < - 5 - 1$

Subtract $1$ from $- 5$ .

$- 10 < - 2 z < - 6$

Step 2

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

$\frac{- 10}{- 2} > \frac{- 2 z}{- 2} > \frac{- 6}{- 2}$

Step 3

Divide $- 10$ by $- 2$ .

$5 > \frac{- 2 z}{- 2} > \frac{- 6}{- 2}$

Step 4

Cancel the common factor of $- 2$ .

Cancel the common factor.

$5 > \frac{- 2 z}{- 2} > \frac{- 6}{- 2}$

Divide $z$ by $1$ .

$5 > z > \frac{- 6}{- 2}$

Step 5

Divide $- 6$ by $- 2$ .

$5 > z > 3$

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.

$3 < z < 5$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$3 < z < 5$

Interval Notation:

$(3, 5)$

Step 8