Solve for n |-2-4n|=34

$| - 2 - 4 n | = 34$

Step 1

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

$- 2 - 4 n = \pm 34$

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.

$- 2 - 4 n = 34$

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

Add $2$ to both sides of the equation.

$- 4 n = 34 + 2$

Add $34$ and $2$ .

$- 4 n = 36$

Divide each term in $- 4 n = 36$ by $- 4$ and simplify.

Divide each term in $- 4 n = 36$ by $- 4$ .

$\frac{- 4 n}{- 4} = \frac{36}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 n}{- 4} = \frac{36}{- 4}$

Divide $n$ by $1$ .

$n = \frac{36}{- 4}$

Simplify the right side.

Divide $36$ by $- 4$ .

$n = - 9$

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

$- 2 - 4 n = - 34$

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

Add $2$ to both sides of the equation.

$- 4 n = - 34 + 2$

Add $- 34$ and $2$ .

$- 4 n = - 32$

Divide each term in $- 4 n = - 32$ by $- 4$ and simplify.

Divide each term in $- 4 n = - 32$ by $- 4$ .

$\frac{- 4 n}{- 4} = \frac{- 32}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 n}{- 4} = \frac{- 32}{- 4}$

Divide $n$ by $1$ .

$n = \frac{- 32}{- 4}$

Simplify the right side.

Divide $- 32$ by $- 4$ .

$n = 8$

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

$n = - 9, 8$

Solve for n |-2-4n|=34

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