# How do you solve x/4-(3x)/2=-1/2?

Apr 12, 2018

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

#### Explanation:

$\implies \frac{x}{4} - \frac{3 x}{2} = - \frac{1}{2}$

$\implies \frac{x}{4} - \frac{3 x}{2} \cdot \frac{2}{2} = - \frac{1}{2}$

$\implies \frac{x}{4} - \frac{6 x}{4} = - \frac{1}{2}$

$\implies - \frac{5 x}{4} = - \frac{1}{2}$

$\implies \frac{5 x}{4} = \frac{1}{2}$

$\implies \frac{5 x}{4} \cdot 4 = \frac{1}{2} \cdot 4$

$\implies 5 x = \frac{4}{2}$

$\implies 5 x = 2$

$\implies \textcolor{b l u e}{x = \frac{2}{5}}$

Apr 12, 2018

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

#### Explanation:

Now this might bring a tear to your eye, but we need to kill the denominators, they're evil.
First you need to find the LCD (Lowest common denominator)
In this case the lowest number that can take out all of the denominators is $4$.
The next thing you need to do is multiply $4$ to everything:
$4 \left(\frac{x}{4}\right) - 4 \left(3 \frac{x}{2}\right) = 4 \left(- \frac{1}{2}\right)$
What this does is cancel out all of the denominators and makes this problem soooooo much easier.
When you divide everything out you will get:
$x - 2 \left(3 x\right) = 2 \left(- 1\right)$
Notice how I divided the $4$ that I multiplied to everything by the denominators of everything.
The next step is mutiplying the rest of the numbers:
$x - 6 x = - 2$
Looks easy now right!?
Now just add the $x ' s$ together and divide:
$- 5 x = - 2$
$x = \frac{2}{5}$