Solve for z -20<-3z-2<10

$- 20 < - 3 z - 2 < 10$

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.

$- 20 + 2 < - 3 z < 10 + 2$

Add $- 20$ and $2$ .

$- 18 < - 3 z < 10 + 2$

Add $10$ and $2$ .

$- 18 < - 3 z < 12$

Step 2

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

$\frac{- 18}{- 3} > \frac{- 3 z}{- 3} > \frac{12}{- 3}$

Step 3

Divide $- 18$ by $- 3$ .

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

Step 4

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $z$ by $1$ .

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

Step 5

Divide $12$ by $- 3$ .

$6 > z > - 4$

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.

$- 4 < z < 6$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 4 < z < 6$

Interval Notation:

$(- 4, 6)$

Step 8