Solve for f |f+10|=1

$| f + 10 | = 1$

Step 1

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

$f + 10 = \pm 1$

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.

$f + 10 = 1$

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

Subtract $10$ from both sides of the equation.

$f = 1 - 10$

Subtract $10$ from $1$ .

$f = - 9$

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

$f + 10 = - 1$

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

Subtract $10$ from both sides of the equation.

$f = - 1 - 10$

Subtract $10$ from $- 1$ .

$f = - 11$

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

$f = - 9, - 11$