# How do you solve the equation abs(5(1-x))=3?

Apr 25, 2017

See the entire solution process below:

#### Explanation:

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)

$5 \left(1 - x\right) = - 3$

$\left(5 \cdot 1\right) - \left(5 \cdot x\right) = - 3$

$5 - 5 x = - 3$

$- \textcolor{red}{5} + 5 - 5 x = - \textcolor{red}{5} - 3$

$0 - 5 x = - 8$

$- 5 x = - 8$

$\frac{- 5 x}{\textcolor{red}{- 5}} = \frac{- 8}{\textcolor{red}{- 5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 5}}} x}{\cancel{\textcolor{red}{- 5}}} = \frac{8}{5}$

$x = \frac{8}{5}$

Solution 2)

$5 \left(1 - x\right) = 3$

$\left(5 \cdot 1\right) - \left(5 \cdot x\right) = 3$

$5 - 5 x = 3$

$- \textcolor{red}{5} + 5 - 5 x = - \textcolor{red}{5} + 3$

$0 - 5 x = - 2$

$- 5 x = - 2$

$\frac{- 5 x}{\textcolor{red}{- 5}} = \frac{- 2}{\textcolor{red}{- 5}}$

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

$x = \frac{2}{5}$

The solution is: $x = \frac{8}{5}$ and $x = \frac{2}{5}$