Solve for z -7<2z+3<9

$- 7 < 2 z + 3 < 9$

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.

$- 7 - 3 < 2 z < 9 - 3$

Subtract $3$ from $- 7$ .

$- 10 < 2 z < 9 - 3$

Subtract $3$ from $9$ .

$- 10 < 2 z < 6$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 10}{2} < \frac{2 z}{2} < \frac{6}{2}$

Step 3

Divide $- 10$ by $2$ .

$- 5 < \frac{2 z}{2} < \frac{6}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- 5 < \frac{2 z}{2} < \frac{6}{2}$

Divide $z$ by $1$ .

$- 5 < z < \frac{6}{2}$

Step 5

Divide $6$ by $2$ .

$- 5 < z < 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 5 < z < 3$

Interval Notation:

$(- 5, 3)$

Step 7