Solve for p 3<2p-3<=12

$3 < 2 p - 3 \leq 12$

Step 1

Move all terms not containing $p$ from the center section of the inequality.

Add $3$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$3 + 3 < 2 p \leq 12 + 3$

Add $3$ and $3$ .

$6 < 2 p \leq 12 + 3$

Add $12$ and $3$ .

$6 < 2 p \leq 15$

Step 2

Divide each term in the inequality by $2$ .

$\frac{6}{2} < \frac{2 p}{2} \leq \frac{15}{2}$

Step 3

Divide $6$ by $2$ .

$3 < \frac{2 p}{2} \leq \frac{15}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$3 < \frac{2 p}{2} \leq \frac{15}{2}$

Divide $p$ by $1$ .

$3 < p \leq \frac{15}{2}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$3 < p \leq \frac{15}{2}$

Interval Notation:

$(3, \frac{15}{2}]$

Step 6