Solve for p 4/(|p|)+12=14

$\frac{4}{| p |} + 12 = 14$

Multiply both sides by $| p |$ .

$\frac{4}{| p |} | p | = 2 | p |$

Simplify the left side.

Cancel the common factor of $| p |$ .

Cancel the common factor.

$\frac{4}{| p |} | p | = 2 | p |$

Rewrite the expression.

$4 = 2 | p |$

Solve for $p$ .

Rewrite the equation as $2 | p | = 4$ .

$2 | p | = 4$

Divide each term in $2 | p | = 4$ by $2$ and simplify.

Divide each term in $2 | p | = 4$ by $2$ .

$\frac{2 | p |}{2} = \frac{4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 | p |}{2} = \frac{4}{2}$

Divide $| p |$ by $1$ .

$| p | = \frac{4}{2}$

Simplify the right side.

Divide $4$ by $2$ .

$| p | = 2$

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

$p = \pm 2$

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.

$p = 2$

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

$p = - 2$

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

$p = 2, - 2$