Solve for y 11=|y/10|

$11 = | \frac{y}{10} |$

Rewrite the equation as $| \frac{y}{10} | = 11$ .

$| \frac{y}{10} | = 11$

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

$\frac{y}{10} = \pm 11$

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.

$\frac{y}{10} = 11$

Multiply both sides of the equation by $10$ .

$10 \frac{y}{10} = 10 \cdot 11$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$10 \frac{y}{10} = 10 \cdot 11$

Rewrite the expression.

$y = 10 \cdot 11$

Simplify the right side.

Multiply $10$ by $11$ .

$y = 110$

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

$\frac{y}{10} = - 11$

Multiply both sides of the equation by $10$ .

$10 \frac{y}{10} = 10 \cdot - 11$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$10 \frac{y}{10} = 10 \cdot - 11$

Rewrite the expression.

$y = 10 \cdot - 11$

Simplify the right side.

Multiply $10$ by $- 11$ .

$y = - 110$

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

$y = 110, - 110$