Solve the Absolute Value Inequality for x (|x+6|)/7=2

$\frac{| x + 6 |}{7} = 2$

Multiply both sides of the equation by $7$ .

$7 \frac{| x + 6 |}{7} = 7 \cdot 2$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$7 \frac{| x + 6 |}{7} = 7 \cdot 2$

Rewrite the expression.

$| x + 6 | = 7 \cdot 2$

Simplify the right side.

Multiply $7$ by $2$ .

$| x + 6 | = 14$

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

$x + 6 = \pm 14$

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.

$x + 6 = 14$

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

Subtract $6$ from both sides of the equation.

$x = 14 - 6$

Subtract $6$ from $14$ .

$x = 8$

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

$x + 6 = - 14$

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

Subtract $6$ from both sides of the equation.

$x = - 14 - 6$

Subtract $6$ from $- 14$ .

$x = - 20$

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

$x = 8, - 20$