Solve the Absolute Value Inequality for x (|x+1|)/3=3

$\frac{| x + 1 |}{3} = 3$

Multiply both sides of the equation by $3$ .

$3 \frac{| x + 1 |}{3} = 3 \cdot 3$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{| x + 1 |}{3} = 3 \cdot 3$

Rewrite the expression.

$| x + 1 | = 3 \cdot 3$

Simplify the right side.

Multiply $3$ by $3$ .

$| x + 1 | = 9$

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

$x + 1 = \pm 9$

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.

$x + 1 = 9$

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

Subtract $1$ from both sides of the equation.

$x = 9 - 1$

Subtract $1$ from $9$ .

$x = 8$

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

$x + 1 = - 9$

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

Subtract $1$ from both sides of the equation.

$x = - 9 - 1$

Subtract $1$ from $- 9$ .

$x = - 10$

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

$x = 8, - 10$