# How do you evaluate \frac { 3x - 4} { 5} - \frac { x + 1} { 4} = \frac { 2x - 4} { 3}?

##### 1 Answer
Jan 7, 2018

$x = \setminus \frac{17}{19}$

#### Explanation:

$\setminus \frac{3 x - 4}{5} - \setminus \frac{x + 1}{4} = \setminus \frac{2 x - 4}{3}$

Let's multiply every fraction by $60$ that is the Least Common Multiplier:
$\setminus \frac{3 x - 4}{5} \cdot 60 - \setminus \frac{x + 1}{4} \cdot 60 = \setminus \frac{2 x - 4}{3} \cdot 60$

Now remove the denominator with the semplification:
$\left(3 x - 4\right) \cdot 12 - \left(x + 1\right) \cdot 15 = \left(2 x - 4\right) \cdot 20$

$36 x - 48 - 15 x - 15 = 40 x - 80$

Move all the terms with the $x$ to the left, and all the constants to the right by changing sign in both cases:
$36 x - 15 x - 40 x = 48 + 15 - 80$

$- 19 x = - 17$

Multiply by $- 1$, so in this way we obtain a positive x:
$- 19 x \cdot \left(- 1\right) = - 17 \cdot \left(- 1\right)$
$19 x = 17$

Final result
$x = \setminus \frac{17}{19}$