Solve the Absolute Value Inequality for x |x+4|+3=17

$| x + 4 | + 3 = 17$

Step 1

Move all terms not containing $| x + 4 |$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$| x + 4 | = 17 - 3$

Subtract $3$ from $17$ .

$| x + 4 | = 14$

Step 2

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

$x + 4 = \pm 14$

Step 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.

$x + 4 = 14$

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

Subtract $4$ from both sides of the equation.

$x = 14 - 4$

Subtract $4$ from $14$ .

$x = 10$

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

$x + 4 = - 14$

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

Subtract $4$ from both sides of the equation.

$x = - 14 - 4$

Subtract $4$ from $- 14$ .

$x = - 18$

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

$x = 10, - 18$