# How do you solve 2-5abs(5m-5)=-73?

Feb 26, 2017

See the entire solution process below:

#### Explanation:

First, subtract $\textcolor{red}{2}$ from each side of the equation to isolate the term with the absolute value while keeping the equation balanced:

$- \textcolor{red}{2} + 2 - 5 \left\mid 5 m - 5 \right\mid = - \textcolor{red}{2} - 73$

$0 - 5 \left\mid 5 m - 5 \right\mid = - 75$

$- 5 \left\mid 5 m - 5 \right\mid = - 75$

Next, divide each side of the equation by $\textcolor{red}{- 5}$ to isolate the absolute value term while keeping the equation balanced:

$\frac{- 5 \left\mid 5 m - 5 \right\mid}{\textcolor{red}{- 5}} = - \frac{75}{\textcolor{red}{- 5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 5}}} \left\mid 5 m - 5 \right\mid}{\cancel{\textcolor{red}{- 5}}} = 15$

$\left\mid 5 m - 5 \right\mid = 15$

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

Solution 1)

$5 m - 5 = - 15$

$5 m - 5 + \textcolor{red}{5} = - 15 + \textcolor{red}{5}$

$5 m - 0 = - 10$

$5 m = - 10$

$\frac{5 m}{\textcolor{red}{5}} = - \frac{10}{\textcolor{red}{5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} m}{\cancel{\textcolor{red}{5}}} = - 2$

$m = - 2$

Solution 2)

$5 m - 5 = 15$

$5 m - 5 + \textcolor{red}{5} = 15 + \textcolor{red}{5}$

$5 m - 0 = 20$

$5 m = 20$

$\frac{5 m}{\textcolor{red}{5}} = \frac{20}{\textcolor{red}{5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} m}{\cancel{\textcolor{red}{5}}} = 4$

$m = 4$

The solution is $m = - 2$ and $m = 4$