Solve for y 10=|y-9|

$10 = | y - 9 |$

Step 1

Rewrite the equation as $| y - 9 | = 10$ .

$| y - 9 | = 10$

Step 2

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

$y - 9 = \pm 10$

Step 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.

$y - 9 = 10$

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

Add $9$ to both sides of the equation.

$y = 10 + 9$

Add $10$ and $9$ .

$y = 19$

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

$y - 9 = - 10$

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

Add $9$ to both sides of the equation.

$y = - 10 + 9$

Add $- 10$ and $9$ .

$y = - 1$

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

$y = 19, - 1$