Solve the Absolute Value Inequality for p |7+p|=7

$| 7 + p | = 7$

Step 1

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

$7 + p = \pm 7$

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.

$7 + p = 7$

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

Subtract $7$ from both sides of the equation.

$p = 7 - 7$

Subtract $7$ from $7$ .

$p = 0$

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

$7 + p = - 7$

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

Subtract $7$ from both sides of the equation.

$p = - 7 - 7$

Subtract $7$ from $- 7$ .

$p = - 14$

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

$p = 0, - 14$