Solve for a |a/11|=7

$| \frac{a}{11} | = 7$

Step 1

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

$\frac{a}{11} = \pm 7$

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.

$\frac{a}{11} = 7$

Multiply both sides of the equation by $11$ .

$11 \frac{a}{11} = 11 \cdot 7$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$11 \frac{a}{11} = 11 \cdot 7$

Rewrite the expression.

$a = 11 \cdot 7$

Simplify the right side.

Multiply $11$ by $7$ .

$a = 77$

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

$\frac{a}{11} = - 7$

Multiply both sides of the equation by $11$ .

$11 \frac{a}{11} = 11 \cdot - 7$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$11 \frac{a}{11} = 11 \cdot - 7$

Rewrite the expression.

$a = 11 \cdot - 7$

Simplify the right side.

Multiply $11$ by $- 7$ .

$a = - 77$

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

$a = 77, - 77$