Solve for p |-5p|=35

$| - 5 p | = 35$

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

$- 5 p = \pm 35$

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.

$- 5 p = 35$

Divide each term in $- 5 p = 35$ by $- 5$ and simplify.

Divide each term in $- 5 p = 35$ by $- 5$ .

$\frac{- 5 p}{- 5} = \frac{35}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 p}{- 5} = \frac{35}{- 5}$

Divide $p$ by $1$ .

$p = \frac{35}{- 5}$

Simplify the right side.

Divide $35$ by $- 5$ .

$p = - 7$

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

$- 5 p = - 35$

Divide each term in $- 5 p = - 35$ by $- 5$ and simplify.

Divide each term in $- 5 p = - 35$ by $- 5$ .

$\frac{- 5 p}{- 5} = \frac{- 35}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 p}{- 5} = \frac{- 35}{- 5}$

Divide $p$ by $1$ .

$p = \frac{- 35}{- 5}$

Simplify the right side.

Divide $- 35$ by $- 5$ .

$p = 7$

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

$p = - 7, 7$