Solve for p -32<6p+10<=-20

$- 32 < 6 p + 10 \leq - 20$

Step 1

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

Subtract $10$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 32 - 10 < 6 p \leq - 20 - 10$

Subtract $10$ from $- 32$ .

$- 42 < 6 p \leq - 20 - 10$

Subtract $10$ from $- 20$ .

$- 42 < 6 p \leq - 30$

Step 2

Divide each term in the inequality by $6$ .

$\frac{- 42}{6} < \frac{6 p}{6} \leq \frac{- 30}{6}$

Step 3

Divide $- 42$ by $6$ .

$- 7 < \frac{6 p}{6} \leq \frac{- 30}{6}$

Step 4

Cancel the common factor of $6$ .

Cancel the common factor.

$- 7 < \frac{6 p}{6} \leq \frac{- 30}{6}$

Divide $p$ by $1$ .

$- 7 < p \leq \frac{- 30}{6}$

Step 5

Divide $- 30$ by $6$ .

$- 7 < p \leq - 5$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 7 < p \leq - 5$

Interval Notation:

$(- 7, - 5]$

Step 7