Solve the Inequality for z 7<z/2+3

$7 < \frac{z}{2} + 3$

Rewrite so $z$ is on the left side of the inequality.

$\frac{z}{2} + 3 > 7$

Move all terms not containing $z$ to the right side of the inequality.

Subtract $3$ from both sides of the inequality.

$\frac{z}{2} > 7 - 3$

Subtract $3$ from $7$ .

$\frac{z}{2} > 4$

Multiply both sides by $2$ .

$\frac{z}{2} \cdot 2 > 4 \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{z}{2} \cdot 2 > 4 \cdot 2$

Rewrite the expression.

$z > 4 \cdot 2$

Simplify the right side.

Multiply $4$ by $2$ .

$z > 8$

The result can be shown in multiple forms.

Inequality Form:

$z > 8$

Interval Notation:

$(8, \infty)$