Solve for z 3|z+7|=12

$3 | z + 7 | = 12$

Divide each term in $3 | z + 7 | = 12$ by $3$ and simplify.

Divide each term in $3 | z + 7 | = 12$ by $3$ .

$\frac{3 | z + 7 |}{3} = \frac{12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 | z + 7 |}{3} = \frac{12}{3}$

Divide $| z + 7 |$ by $1$ .

$| z + 7 | = \frac{12}{3}$

Simplify the right side.

Divide $12$ by $3$ .

$| z + 7 | = 4$

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

$z + 7 = \pm 4$

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.

$z + 7 = 4$

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

Subtract $7$ from both sides of the equation.

$z = 4 - 7$

Subtract $7$ from $4$ .

$z = - 3$

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

$z + 7 = - 4$

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

Subtract $7$ from both sides of the equation.

$z = - 4 - 7$

Subtract $7$ from $- 4$ .

$z = - 11$

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

$z = - 3, - 11$