Solve the Absolute Value Inequality for n 7|n|=56

$7 | n | = 56$

Step 1

Divide each term in $7 | n | = 56$ by $7$ and simplify.

Divide each term in $7 | n | = 56$ by $7$ .

$\frac{7 | n |}{7} = \frac{56}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 | n |}{7} = \frac{56}{7}$

Divide $| n |$ by $1$ .

$| n | = \frac{56}{7}$

Simplify the right side.

Divide $56$ by $7$ .

$| n | = 8$

Step 2

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

$n = \pm 8$

Step 3

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.

$n = 8$

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

$n = - 8$

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

$n = 8, - 8$