Solve the Absolute Value Inequality for x |x-3|=1

$| x - 3 | = 1$

Step 1

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

$x - 3 = \pm 1$

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.

$x - 3 = 1$

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

Add $3$ to both sides of the equation.

$x = 1 + 3$

Add $1$ and $3$ .

$x = 4$

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

$x - 3 = - 1$

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

Add $3$ to both sides of the equation.

$x = - 1 + 3$

Add $- 1$ and $3$ .

$x = 2$

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

$x = 4, 2$