Solve for n -5|6n+15|+2=-43

$- 5 | 6 n + 15 | + 2 = - 43$

Step 1

Move all terms not containing $| 6 n + 15 |$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$- 5 | 6 n + 15 | = - 43 - 2$

Subtract $2$ from $- 43$ .

$- 5 | 6 n + 15 | = - 45$

Step 2

Divide each term in $- 5 | 6 n + 15 | = - 45$ by $- 5$ and simplify.

Divide each term in $- 5 | 6 n + 15 | = - 45$ by $- 5$ .

$\frac{- 5 | 6 n + 15 |}{- 5} = \frac{- 45}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 | 6 n + 15 |}{- 5} = \frac{- 45}{- 5}$

Divide $| 6 n + 15 |$ by $1$ .

$| 6 n + 15 | = \frac{- 45}{- 5}$

Simplify the right side.

Divide $- 45$ by $- 5$ .

$| 6 n + 15 | = 9$

Step 3

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

$6 n + 15 = \pm 9$

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.

$6 n + 15 = 9$

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

Subtract $15$ from both sides of the equation.

$6 n = 9 - 15$

Subtract $15$ from $9$ .

$6 n = - 6$

Divide each term in $6 n = - 6$ by $6$ and simplify.

Divide each term in $6 n = - 6$ by $6$ .

$\frac{6 n}{6} = \frac{- 6}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 n}{6} = \frac{- 6}{6}$

Divide $n$ by $1$ .

$n = \frac{- 6}{6}$

Simplify the right side.

Divide $- 6$ by $6$ .

$n = - 1$

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

$6 n + 15 = - 9$

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

Subtract $15$ from both sides of the equation.

$6 n = - 9 - 15$

Subtract $15$ from $- 9$ .

$6 n = - 24$

Divide each term in $6 n = - 24$ by $6$ and simplify.

Divide each term in $6 n = - 24$ by $6$ .

$\frac{6 n}{6} = \frac{- 24}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 n}{6} = \frac{- 24}{6}$

Divide $n$ by $1$ .

$n = \frac{- 24}{6}$

Simplify the right side.

Divide $- 24$ by $6$ .

$n = - 4$

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

$n = - 1, - 4$

Solve for n -5|6n+15|+2=-43

Related Questions

Support LCMGCF.com by disabling your adblocker.