Solve the Absolute Value Inequality for k |k-10|=3

$| k - 10 | = 3$

Step 1

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

$k - 10 = \pm 3$

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.

$k - 10 = 3$

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

Add $10$ to both sides of the equation.

$k = 3 + 10$

Add $3$ and $10$ .

$k = 13$

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

$k - 10 = - 3$

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

Add $10$ to both sides of the equation.

$k = - 3 + 10$

Add $- 3$ and $10$ .

$k = 7$

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

$k = 13, 7$