Solve for z -5<2z+3<15

$- 5 < 2 z + 3 < 15$

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.

$- 5 - 3 < 2 z < 15 - 3$

Subtract $3$ from $- 5$ .

$- 8 < 2 z < 15 - 3$

Subtract $3$ from $15$ .

$- 8 < 2 z < 12$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 8}{2} < \frac{2 z}{2} < \frac{12}{2}$

Step 3

Divide $- 8$ by $2$ .

$- 4 < \frac{2 z}{2} < \frac{12}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- 4 < \frac{2 z}{2} < \frac{12}{2}$

Divide $z$ by $1$ .

$- 4 < z < \frac{12}{2}$

Step 5

Divide $12$ by $2$ .

$- 4 < z < 6$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 4 < z < 6$

Interval Notation:

$(- 4, 6)$

Step 7