Solve the Absolute Value Inequality for b |b+3|-1=2

$| b + 3 | - 1 = 2$

Move all terms not containing $| b + 3 |$ to the right side of the equation.

Add $1$ to both sides of the equation.

$| b + 3 | = 2 + 1$

Add $2$ and $1$ .

$| b + 3 | = 3$

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

$b + 3 = \pm 3$

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.

$b + 3 = 3$

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

Subtract $3$ from both sides of the equation.

$b = 3 - 3$

Subtract $3$ from $3$ .

$b = 0$

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

$b + 3 = - 3$

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

Subtract $3$ from both sides of the equation.

$b = - 3 - 3$

Subtract $3$ from $- 3$ .

$b = - 6$

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

$b = 0, - 6$