Solve for z -17<-3z-2<16

$- 17 < - 3 z - 2 < 16$

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.

$- 17 + 2 < - 3 z < 16 + 2$

Add $- 17$ and $2$ .

$- 15 < - 3 z < 16 + 2$

Add $16$ and $2$ .

$- 15 < - 3 z < 18$

Step 2

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

$\frac{- 15}{- 3} > \frac{- 3 z}{- 3} > \frac{18}{- 3}$

Step 3

Divide $- 15$ by $- 3$ .

$5 > \frac{- 3 z}{- 3} > \frac{18}{- 3}$

Step 4

Cancel the common factor of $- 3$ .

Cancel the common factor.

$5 > \frac{- 3 z}{- 3} > \frac{18}{- 3}$

Divide $z$ by $1$ .

$5 > z > \frac{18}{- 3}$

Step 5

Divide $18$ by $- 3$ .

$5 > z > - 6$

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.

$- 6 < z < 5$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 6 < z < 5$

Interval Notation:

$(- 6, 5)$

Step 8