Solve the System of Inequalities -3<=p/2<0

$- 3 \leq \frac{p}{2} < 0$

Step 1

Solve $- 3 \leq \frac{p}{2}$ for $p$ .

Multiply both sides by $2$ .

$- 3 \cdot 2 \leq \frac{p}{2} \cdot 2$

Simplify.

Simplify the left side.

Multiply $- 3$ by $2$ .

$- 6 \leq \frac{p}{2} \cdot 2$

Simplify the right side.

Cancel the common factor of $2$ .

Cancel the common factor.

$- 6 \leq \frac{p}{2} \cdot 2$

Rewrite the expression.

$- 6 \leq p$

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

$p \geq - 6$

Step 2

Solve $\frac{p}{2} < 0$ for $p$ .

Multiply both sides by $2$ .

$\frac{p}{2} \cdot 2 < 0 \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{p}{2} \cdot 2 < 0 \cdot 2$

Rewrite the expression.

$p < 0 \cdot 2$

Simplify the right side.

Multiply $0$ by $2$ .

$p < 0$

Step 3

Find the intersection of $p \geq - 6$ and $p < 0$ .

$- 6 \leq p < 0$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 6 \leq p < 0$

Interval Notation:

$[- 6, 0)$

Step 5