# How do you solve 20/x=-5/2?

Dec 5, 2016

$x = - 8$

#### Explanation:

First, you need to multiply each side by a common denominator to eliminate the fractions and keep the equation balanced. In this case the common denominator is $2 x$:

$\frac{\left(2 x\right) \cdot 20}{x} = - \frac{2 x \cdot - 5}{2}$

$\frac{\left(2 \cancel{x}\right) \cdot 20}{\cancel{x}} = - \frac{\cancel{2} x \cdot 5}{\cancel{2}}$

$2 \cdot 20 = - 5 x$

$- 5 x = 40$

Now we can solve for $x$ while keeping the equation balanced:

$\frac{- 5 x}{-} 5 = \frac{40}{- 5}$

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

$x = - 8$

Dec 5, 2016

$x = - 8$

#### Explanation:

When we have a fraction equal to another fraction, we can solve using the method of $\textcolor{b l u e}{\text{cross-multiplication}}$

The negative sign on the right side must be attached to either the 5 or the 2 but NOT BOTH. as this would give a positive result. I'm attaching it to the 2.

$\Rightarrow \frac{\textcolor{b l u e}{20}}{\textcolor{red}{x}} = \frac{\textcolor{red}{5}}{\textcolor{b l u e}{- 2}}$

To cross-multiply, multiply the terms in $\textcolor{red}{\text{red}}$ and the terms in $\textcolor{b l u e}{\text{blue}}$ and equate them.

$\Rightarrow \textcolor{red}{5 x} = \left(\textcolor{b l u e}{20} \times \textcolor{b l u e}{- 2}\right)$

$\Rightarrow 5 x = - 40$

To solve for x, divide both sides by 5

$\frac{\cancel{5} x}{\cancel{5}} = \frac{- 40}{5}$

$\Rightarrow x = - 8 \text{ is the solution}$