Solve for p |-9p-585|=225

$| - 9 p - 585 | = 225$

Step 1

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

$- 9 p - 585 = \pm 225$

Step 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.

$- 9 p - 585 = 225$

Move all terms not containing $p$ to the right side of the equation.

Add $585$ to both sides of the equation.

$- 9 p = 225 + 585$

Add $225$ and $585$ .

$- 9 p = 810$

Divide each term in $- 9 p = 810$ by $- 9$ and simplify.

Divide each term in $- 9 p = 810$ by $- 9$ .

$\frac{- 9 p}{- 9} = \frac{810}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 p}{- 9} = \frac{810}{- 9}$

Divide $p$ by $1$ .

$p = \frac{810}{- 9}$

Simplify the right side.

Divide $810$ by $- 9$ .

$p = - 90$

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

$- 9 p - 585 = - 225$

Move all terms not containing $p$ to the right side of the equation.

Add $585$ to both sides of the equation.

$- 9 p = - 225 + 585$

Add $- 225$ and $585$ .

$- 9 p = 360$

Divide each term in $- 9 p = 360$ by $- 9$ and simplify.

Divide each term in $- 9 p = 360$ by $- 9$ .

$\frac{- 9 p}{- 9} = \frac{360}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 p}{- 9} = \frac{360}{- 9}$

Divide $p$ by $1$ .

$p = \frac{360}{- 9}$

Simplify the right side.

Divide $360$ by $- 9$ .

$p = - 40$

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

$p = - 90, - 40$

Solve for p |-9p-585|=225

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