Solve the Absolute Value Inequality for p -3|p|=-12

$- 3 | p | = - 12$

Divide each term in $- 3 | p | = - 12$ by $- 3$ and simplify.

Divide each term in $- 3 | p | = - 12$ by $- 3$ .

$\frac{- 3 | p |}{- 3} = \frac{- 12}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 | p |}{- 3} = \frac{- 12}{- 3}$

Divide $| p |$ by $1$ .

$| p | = \frac{- 12}{- 3}$

Simplify the right side.

Divide $- 12$ by $- 3$ .

$| p | = 4$

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$p = \pm 4$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$p = 4$

Next, use the negative value of the $\pm$ to find the second solution.

$p = - 4$

The complete solution is the result of both the positive and negative portions of the solution.

$p = 4, - 4$