Solve the Inequality for p -5<3p+7<=22

$- 5 < 3 p + 7 \leq 22$

Step 1

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

Subtract $7$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 5 - 7 < 3 p \leq 22 - 7$

Subtract $7$ from $- 5$ .

$- 12 < 3 p \leq 22 - 7$

Subtract $7$ from $22$ .

$- 12 < 3 p \leq 15$

Step 2

Divide each term in the inequality by $3$ .

$\frac{- 12}{3} < \frac{3 p}{3} \leq \frac{15}{3}$

Step 3

Divide $- 12$ by $3$ .

$- 4 < \frac{3 p}{3} \leq \frac{15}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$- 4 < \frac{3 p}{3} \leq \frac{15}{3}$

Divide $p$ by $1$ .

$- 4 < p \leq \frac{15}{3}$

Step 5

Divide $15$ by $3$ .

$- 4 < p \leq 5$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 4 < p \leq 5$

Interval Notation:

$(- 4, 5]$

Step 7