Solve for z 10<3z+4<22

$10 < 3 z + 4 < 22$

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.

$10 - 4 < 3 z < 22 - 4$

Subtract $4$ from $10$ .

$6 < 3 z < 22 - 4$

Subtract $4$ from $22$ .

$6 < 3 z < 18$

Step 2

Divide each term in the inequality by $3$ .

$\frac{6}{3} < \frac{3 z}{3} < \frac{18}{3}$

Step 3

Divide $6$ by $3$ .

$2 < \frac{3 z}{3} < \frac{18}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$2 < \frac{3 z}{3} < \frac{18}{3}$

Divide $z$ by $1$ .

$2 < z < \frac{18}{3}$

Step 5

Divide $18$ by $3$ .

$2 < z < 6$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$2 < z < 6$

Interval Notation:

$(2, 6)$

Step 7