Solve for t |t+5|=8

$| t + 5 | = 8$

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

$t + 5 = \pm 8$

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.

$t + 5 = 8$

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

Subtract $5$ from both sides of the equation.

$t = 8 - 5$

Subtract $5$ from $8$ .

$t = 3$

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

$t + 5 = - 8$

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

Subtract $5$ from both sides of the equation.

$t = - 8 - 5$

Subtract $5$ from $- 8$ .

$t = - 13$

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

$t = 3, - 13$