Solve for n 5-8|-2n|=-75

$5 - 8 | - 2 n | = - 75$

Step 1

Move all terms not containing $| - 2 n |$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$- 8 | - 2 n | = - 75 - 5$

Subtract $5$ from $- 75$ .

$- 8 | - 2 n | = - 80$

Step 2

Divide each term in $- 8 | - 2 n | = - 80$ by $- 8$ and simplify.

Divide each term in $- 8 | - 2 n | = - 80$ by $- 8$ .

$\frac{- 8 | - 2 n |}{- 8} = \frac{- 80}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 | - 2 n |}{- 8} = \frac{- 80}{- 8}$

Divide $| - 2 n |$ by $1$ .

$| - 2 n | = \frac{- 80}{- 8}$

Simplify the right side.

Divide $- 80$ by $- 8$ .

$| - 2 n | = 10$

Step 3

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

$- 2 n = \pm 10$

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.

$- 2 n = 10$

Divide each term in $- 2 n = 10$ by $- 2$ and simplify.

Divide each term in $- 2 n = 10$ by $- 2$ .

$\frac{- 2 n}{- 2} = \frac{10}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 n}{- 2} = \frac{10}{- 2}$

Divide $n$ by $1$ .

$n = \frac{10}{- 2}$

Simplify the right side.

Divide $10$ by $- 2$ .

$n = - 5$

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

$- 2 n = - 10$

Divide each term in $- 2 n = - 10$ by $- 2$ and simplify.

Divide each term in $- 2 n = - 10$ by $- 2$ .

$\frac{- 2 n}{- 2} = \frac{- 10}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 n}{- 2} = \frac{- 10}{- 2}$

Divide $n$ by $1$ .

$n = \frac{- 10}{- 2}$

Simplify the right side.

Divide $- 10$ by $- 2$ .

$n = 5$

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

$n = - 5, 5$

Solve for n 5-8|-2n|=-75

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