Solve for z -8<-3z+4<-2

$- 8 < - 3 z + 4 < - 2$

Step 1

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

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

$- 8 - 4 < - 3 z < - 2 - 4$

Subtract $4$ from $- 8$ .

$- 12 < - 3 z < - 2 - 4$

Subtract $4$ from $- 2$ .

$- 12 < - 3 z < - 6$

Step 2

Divide each term in the inequality by $- 3$ .

$\frac{- 12}{- 3} > \frac{- 3 z}{- 3} > \frac{- 6}{- 3}$

Step 3

Divide $- 12$ by $- 3$ .

$4 > \frac{- 3 z}{- 3} > \frac{- 6}{- 3}$

Step 4

Cancel the common factor of $- 3$ .

Cancel the common factor.

$4 > \frac{- 3 z}{- 3} > \frac{- 6}{- 3}$

Divide $z$ by $1$ .

$4 > z > \frac{- 6}{- 3}$

Step 5

Divide $- 6$ by $- 3$ .

$4 > z > 2$

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.

$2 < z < 4$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$2 < z < 4$

Interval Notation:

$(2, 4)$

Step 8