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}#