# How do you solve abs(7m)+3=73?

Feb 7, 2017

See the entire solution process below:

#### Explanation:

First, subtract $\textcolor{red}{3}$ from each side of the equation to isolate the absolute value function while keeping the equation balanced:

$\left\mid 7 m \right\mid + 3 - \textcolor{red}{3} = 73 - \textcolor{red}{3}$

$\left\mid 7 m \right\mid + 0 = 70$

$\left\mid 7 m \right\mid = 70$

The absolute value function takes any positive or negative term and transforms it to its positive form. Therefore, we need to solve the term inside the absolute value function for both its negative and positive equivalent.

Solution 1)

$7 m = - 70$

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

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} m}{\cancel{\textcolor{red}{7}}} = - 10$

$m = - 10$

Solution 2)

$7 m = 70$

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

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} m}{\cancel{\textcolor{red}{7}}} = 10$

$m = 10$

The solution is: $m = - 10$ and $m = 10$