How do you solve #\frac { x } { 3} + \frac { 2x + 4} { 4} = \frac { x - 1} { 6} - \frac { 3- 2x } { 2}#?

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Answer 1 · 2016-10-31T00:05:05

Multiply through by a lowest common denominator to find #x=8#.

#x/3 +(2x+4)/4=(x-1)/6 - (3-2x)/2#

Multiply through by the lowest common denominator #color(red)(12)#.

#color(red)(12) * x/3 +color(red)(12) * (2x+4)/4=color(red)(12) * (x-1)/6 - color(red)(12) * (3-2x)/2#

#4x +3(2x+4) = 2(x-1) -6(3-2x)#

#4x+6x+12=2x-2-18+12x#

#color(white)(aaa)10x+12=color(white)(aaa)14x-20#
#color(white)a-14x-12=-14x-12#

#-4x=-32#

#(-4x)/-4=-32/-4#

#x=8#