Solve for z -12<-3z+3<15

$- 12 < - 3 z + 3 < 15$

Step 1

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

Subtract $3$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 12 - 3 < - 3 z < 15 - 3$

Subtract $3$ from $- 12$ .

$- 15 < - 3 z < 15 - 3$

Subtract $3$ from $15$ .

$- 15 < - 3 z < 12$

Step 2

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

$\frac{- 15}{- 3} > \frac{- 3 z}{- 3} > \frac{12}{- 3}$

Step 3

Divide $- 15$ by $- 3$ .

$5 > \frac{- 3 z}{- 3} > \frac{12}{- 3}$

Step 4

Cancel the common factor of $- 3$ .

Cancel the common factor.

$5 > \frac{- 3 z}{- 3} > \frac{12}{- 3}$

Divide $z$ by $1$ .

$5 > z > \frac{12}{- 3}$

Step 5

Divide $12$ by $- 3$ .

$5 > z > - 4$

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