# How do you solve for x in 3/(2-x)=4?

Mar 7, 2018

$x = \frac{5}{4}$

#### Explanation:

Starting from the equation:

$\frac{3}{2 - x} = 4$

We note that the $x$ is in the denominator on the left hand side. We can do at least two things at this point, we can take the reciprocal of both sides or multiply both sides by a factor of $\left(2 - x\right)$. Let's do the multiplication:

$\left(2 - x\right) \cdot \frac{3}{2 - x} = \left(2 - x\right) \cdot 4$

we can cancel the common factor of $\left(2 - x\right)$ on the left, and we can distribute the factor of $4$ across the terms of $\left(2 - x\right)$ on the right to get

$\cancel{\setminus} \textcolor{red}{\left(2 - x\right)} \cdot \frac{3}{\cancel{\setminus}} \textcolor{red}{\left(2 - x\right)} = \left(\setminus \textcolor{b l u e}{4} \cdot 2 - \setminus \textcolor{b l u e}{4} \cdot x\right)$

$3 = 8 - 4 x$

Next we need to get the x alone on one side. Lets subtract $8$ from both sides:

$3 - 8 = 8 - 8 - 4 x$

$- 5 = - 4 x$

Then we can divide both sides by $- 4$

$\frac{- 5}{- 4} = \frac{- 4}{- 4} x$

$\frac{5}{4} = x$

which can be rewritten as

$x = \frac{5}{4}$