How do you solve #\frac { 3x ( x - 2) } { 4} = 2- x#?

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Answer 1 · 2017-05-31T17:38:34

#color(red)(x=2 or x=-4/3#

#(3x(x-2))/4=2-x#

#:.3x(x-2=8-4x#

#:.3x^2-6x=8-4x#

#:.3x^2-6x+4x-8=0#

#:.x^2-2x-8=0#

#:.(x-2)(3x+4)=0#

#:.x-2=0,3x+4=0#

#:.color(red)(x=2 or x=-4/3#

substitute #color(red)(x=-4/3#

#:.(3*color(red)(-4/3)(color(red)(-4/3)-2))/4=2-(color(red)(-4/3))#

#:.((-4)(-4/3-6/3))/4=6/3+4/3#

#:.(-1(-4/3-6/3))/4=6/3+4/3#

#:.10/3=10/3#

substitute #color(red)(x=2#

#:.(3*color(red)2(color(red)2-2))/4=2-color(red)2#

#(6*0)/4=0#

#:.0/4=0#

#:.color(red)(0=0#