Solve for z 6<3z+3<12

$6 < 3 z + 3 < 12$

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.

$6 - 3 < 3 z < 12 - 3$

Subtract $3$ from $6$ .

$3 < 3 z < 12 - 3$

Subtract $3$ from $12$ .

$3 < 3 z < 9$

Step 2

Divide each term in the inequality by $3$ .

$\frac{3}{3} < \frac{3 z}{3} < \frac{9}{3}$

Step 3

Divide $3$ by $3$ .

$1 < \frac{3 z}{3} < \frac{9}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$1 < \frac{3 z}{3} < \frac{9}{3}$

Divide $z$ by $1$ .

$1 < z < \frac{9}{3}$

Step 5

Divide $9$ by $3$ .

$1 < z < 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$1 < z < 3$

Interval Notation:

$(1, 3)$

Step 7