Solve the Absolute Value Inequality for t |t/2|=6

$| \frac{t}{2} | = 6$

Step 1

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

$\frac{t}{2} = \pm 6$

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.

$\frac{t}{2} = 6$

Multiply both sides of the equation by $2$ .

$2 \frac{t}{2} = 2 \cdot 6$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{t}{2} = 2 \cdot 6$

Rewrite the expression.

$t = 2 \cdot 6$

Simplify the right side.

Multiply $2$ by $6$ .

$t = 12$

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

$\frac{t}{2} = - 6$

Multiply both sides of the equation by $2$ .

$2 \frac{t}{2} = 2 \cdot - 6$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{t}{2} = 2 \cdot - 6$

Rewrite the expression.

$t = 2 \cdot - 6$

Simplify the right side.

Multiply $2$ by $- 6$ .

$t = - 12$

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

$t = 12, - 12$