Algebra Examples

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

Step 1

Multiply both sides by $| p |$ .

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

Step 2

Simplify the left side.

Tap for more steps...

Step 2.1

Cancel the common factor of $| p |$ .

Tap for more steps...

Step 2.1.1

Cancel the common factor.

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

Step 2.1.2

Rewrite the expression.

$4 = 2 | p |$

Step 3

Solve for $p$ .

Tap for more steps...

Step 3.1

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

$2 | p | = 4$

Step 3.2

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

Tap for more steps...

Step 3.2.1

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

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

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

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

Step 3.2.2.1.2

Divide $| p |$ by $1$ .

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

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Divide $4$ by $2$ .

$| p | = 2$

Step 3.3

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

$p = \pm 2$

Step 3.4

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

Tap for more steps...

Step 3.4.1

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

$p = 2$

Step 3.4.2

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

$p = - 2$

Step 3.4.3

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

$p = 2, - 2$