# How do you solve -4/(2-x)= -2?

Apr 24, 2017

See the entire solution process below:

#### Explanation:

There are several ways to approach this. My first step is to multiply each side of the equation by $\textcolor{red}{\frac{1}{-} 2}$ to eliminate the negative signs and factor some of the numbers:

$\textcolor{red}{\frac{1}{-} 2} \cdot \frac{- 4}{2 - x} = \textcolor{red}{\frac{1}{-} 2} \cdot - 2$

$\textcolor{red}{\frac{1}{\textcolor{b l a c k}{\cancel{\textcolor{red}{- 2}}}}} \cdot \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 4}}} 2}{2 - x} = \textcolor{red}{\frac{1}{\textcolor{b l a c k}{\cancel{\textcolor{red}{- 2}}}}} \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{- 2}}}$

$\frac{2}{2 - x} = 1$

Next, multiply each side of the equation by $\left(\textcolor{red}{2 - x}\right)$ to eliminate the fraction while keeping the equation balanced:

$\left(\textcolor{red}{2 - x}\right) \cdot \frac{2}{2 - x} = 1 \left(\textcolor{red}{2 - x}\right)$

$\cancel{\left(\textcolor{red}{2 - x}\right)} \cdot \frac{2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2 - x}}}} = 2 - x$

$2 = 2 - x$

Then subtract $\textcolor{red}{2}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$- \textcolor{red}{2} + 2 = - \textcolor{red}{2} + 2 - x$

$0 = 0 - x$

$0 = - x$

Now, multiply each side of the equation by $\textcolor{red}{- 1}$ to solve for $x$ while keeping the equation balanced:

$\textcolor{red}{- 1} \cdot 0 = \textcolor{red}{- 1} \cdot - x$

$0 = x$

$x = 0$