Find All Complex Solutions |-4+5x|=16

$| - 4 + 5 x | = 16$

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

$- 4 + 5 x = \pm 16$

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.

$- 4 + 5 x = 16$

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

Add $4$ to both sides of the equation.

$5 x = 16 + 4$

Add $16$ and $4$ .

$5 x = 20$

Divide each term in $5 x = 20$ by $5$ and simplify.

Divide each term in $5 x = 20$ by $5$ .

$\frac{5 x}{5} = \frac{20}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{20}{5}$

Divide $x$ by $1$ .

$x = \frac{20}{5}$

Simplify the right side.

Divide $20$ by $5$ .

$x = 4$

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

$- 4 + 5 x = - 16$

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

Add $4$ to both sides of the equation.

$5 x = - 16 + 4$

Add $- 16$ and $4$ .

$5 x = - 12$

Divide each term in $5 x = - 12$ by $5$ and simplify.

Divide each term in $5 x = - 12$ by $5$ .

$\frac{5 x}{5} = \frac{- 12}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 12}{5}$

Divide $x$ by $1$ .

$x = \frac{- 12}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{12}{5}$

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

$x = 4, - \frac{12}{5}$