How do you solve #\frac { 1- x } { 2} - \frac { 3} { 5} = \frac { 4} { 3} - \frac { x + 2} { 6}#?

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Answer 1 · 2017-10-31T19:34:54

#x = -3.3#

#(1-x)/2 - 3/5 = 4/3 - (x+2)/6#

find the LCM of between all denominators:

#LCM (2,3,5,6) = 5*6 = 30#

#(1-x)/2 = (15(1-x))/30 = (15-15x)/30#

#3/5 = 18/30#

#4/3 = 40/30#

#(x+2)/6 = (5(x+2))/30 = (5x+10)/30#

#(15-15x)/30 - 18/30 = 40/30 - (5x+10)/30#

multiply all numbers by #30#, removing the denominator:

#15-15x - 18 = 40 - (5x + 10)#

#-15x - 18 = 25 - (5x+10)#

#-15x - 43 = -5x - 10#

#-10x - 43 = -10#

#-10x = 33#

#-x = 3.3#

#x = -3.3#