Solve for n 2|n|-12=16

$2 | n | - 12 = 16$

Step 1

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

Add $12$ to both sides of the equation.

$2 | n | = 16 + 12$

Add $16$ and $12$ .

$2 | n | = 28$

Step 2

Divide each term in $2 | n | = 28$ by $2$ and simplify.

Divide each term in $2 | n | = 28$ by $2$ .

$\frac{2 | n |}{2} = \frac{28}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 | n |}{2} = \frac{28}{2}$

Divide $| n |$ by $1$ .

$| n | = \frac{28}{2}$

Simplify the right side.

Divide $28$ by $2$ .

$| n | = 14$

Step 3

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

$n = \pm 14$

Step 4

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.

$n = 14$

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

$n = - 14$

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

$n = 14, - 14$