Solve for t |t-8|+4=11

$| t - 8 | + 4 = 11$

Move all terms not containing $| t - 8 |$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$| t - 8 | = 11 - 4$

Subtract $4$ from $11$ .

$| t - 8 | = 7$

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

$t - 8 = \pm 7$

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.

$t - 8 = 7$

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

Add $8$ to both sides of the equation.

$t = 7 + 8$

Add $7$ and $8$ .

$t = 15$

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

$t - 8 = - 7$

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

Add $8$ to both sides of the equation.

$t = - 7 + 8$

Add $- 7$ and $8$ .

$t = 1$

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

$t = 15, 1$