Pre-Algebra Examples

$8 | - 9 p | = 72$

Step 1

Divide each term in $8 | - 9 p | = 72$ by $8$ and simplify.

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Step 1.1

Divide each term in $8 | - 9 p | = 72$ by $8$ .

$\frac{8 | - 9 p |}{8} = \frac{72}{8}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $8$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{8 | - 9 p |}{8} = \frac{72}{8}$

Step 1.2.1.2

Divide $| - 9 p |$ by $1$ .

$| - 9 p | = \frac{72}{8}$

Step 1.2.2

Remove non-negative terms from the absolute value.

$9 | p | = \frac{72}{8}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $72$ by $8$ .

$9 | p | = 9$

Step 2

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

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Step 2.1

Divide each term in $9 | p | = 9$ by $9$ .

$\frac{9 | p |}{9} = \frac{9}{9}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $9$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{9 | p |}{9} = \frac{9}{9}$

Step 2.2.1.2

Divide $| p |$ by $1$ .

$| p | = \frac{9}{9}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $9$ by $9$ .

$| p | = 1$

Step 3

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

$p = \pm 1$

Step 4

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

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Step 4.1

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

$p = 1$

Step 4.2

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

$p = - 1$

Step 4.3

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

$p = 1, - 1$