Solve the Absolute Value Inequality for x |x-1|=8

$| x - 1 | = 8$

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

$x - 1 = \pm 8$

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.

$x - 1 = 8$

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

Add $1$ to both sides of the equation.

$x = 8 + 1$

Add $8$ and $1$ .

$x = 9$

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

$x - 1 = - 8$

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

Add $1$ to both sides of the equation.

$x = - 8 + 1$

Add $- 8$ and $1$ .

$x = - 7$

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

$x = 9, - 7$