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

1 Answer
Jan 7, 2018

x=\frac{17}{19}

Explanation:

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

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

Now remove the denominator with the semplification:
(3x-4)*12-(x+1)*15=(2x-4)*20

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

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

-19x = -17

Multiply by -1, so in this way we obtain a positive x:
-19x * (-1) = -17 * (-1)
19x=17

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