Solve the Absolute Value Inequality for m |7m|+3=73

$| 7 m | + 3 = 73$

Move all terms not containing $| 7 m |$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$| 7 m | = 73 - 3$

Subtract $3$ from $73$ .

$| 7 m | = 70$

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

$7 m = \pm 70$

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.

$7 m = 70$

Divide each term in $7 m = 70$ by $7$ and simplify.

Divide each term in $7 m = 70$ by $7$ .

$\frac{7 m}{7} = \frac{70}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 m}{7} = \frac{70}{7}$

Divide $m$ by $1$ .

$m = \frac{70}{7}$

Simplify the right side.

Divide $70$ by $7$ .

$m = 10$

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

$7 m = - 70$

Divide each term in $7 m = - 70$ by $7$ and simplify.

Divide each term in $7 m = - 70$ by $7$ .

$\frac{7 m}{7} = \frac{- 70}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 m}{7} = \frac{- 70}{7}$

Divide $m$ by $1$ .

$m = \frac{- 70}{7}$

Simplify the right side.

Divide $- 70$ by $7$ .

$m = - 10$

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

$m = 10, - 10$