Find All Complex Solutions |x+7|+6=9

$| x + 7 | + 6 = 9$

Move all terms not containing $| x + 7 |$ to the right side of the equation.

Subtract $6$ from both sides of the equation.

$| x + 7 | = 9 - 6$

Subtract $6$ from $9$ .

$| x + 7 | = 3$

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

$x + 7 = \pm 3$

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.

$x + 7 = 3$

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

Subtract $7$ from both sides of the equation.

$x = 3 - 7$

Subtract $7$ from $3$ .

$x = - 4$

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

$x + 7 = - 3$

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

Subtract $7$ from both sides of the equation.

$x = - 3 - 7$

Subtract $7$ from $- 3$ .

$x = - 10$

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

$x = - 4, - 10$