Solve the Absolute Value Inequality for n |-2n+6|=6

$| - 2 n + 6 | = 6$

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

$- 2 n + 6 = \pm 6$

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.

$- 2 n + 6 = 6$

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

Subtract $6$ from both sides of the equation.

$- 2 n = 6 - 6$

Subtract $6$ from $6$ .

$- 2 n = 0$

Divide each term in $- 2 n = 0$ by $- 2$ and simplify.

Divide each term in $- 2 n = 0$ by $- 2$ .

$\frac{- 2 n}{- 2} = \frac{0}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 n}{- 2} = \frac{0}{- 2}$

Divide $n$ by $1$ .

$n = \frac{0}{- 2}$

Simplify the right side.

Divide $0$ by $- 2$ .

$n = 0$

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

$- 2 n + 6 = - 6$

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

Subtract $6$ from both sides of the equation.

$- 2 n = - 6 - 6$

Subtract $6$ from $- 6$ .

$- 2 n = - 12$

Divide each term in $- 2 n = - 12$ by $- 2$ and simplify.

Divide each term in $- 2 n = - 12$ by $- 2$ .

$\frac{- 2 n}{- 2} = \frac{- 12}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 n}{- 2} = \frac{- 12}{- 2}$

Divide $n$ by $1$ .

$n = \frac{- 12}{- 2}$

Simplify the right side.

Divide $- 12$ by $- 2$ .

$n = 6$

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

$n = 0, 6$