Solve for x |x+1|=3

$| x + 1 | = 3$

Step 1

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

$x + 1 = \pm 3$

Step 2

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.

$x + 1 = 3$

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

Subtract $1$ from both sides of the equation.

$x = 3 - 1$

Subtract $1$ from $3$ .

$x = 2$

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

$x + 1 = - 3$

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

Subtract $1$ from both sides of the equation.

$x = - 3 - 1$

Subtract $1$ from $- 3$ .

$x = - 4$

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

$x = 2, - 4$