How do you solve #2(1-2x)/3 -2x = -2/5 + 4(2-3x)/3#?

1 Answer
Feb 28, 2016

Answer:

Taken very gradually

#x=-28/25 -> -1 3/25#

Explanation:

Given:#color(brown)(" "2 (1-2x)/3 -2x=-2/5+4 (2-3x)/3)#...(2)

'~~~~~~~~~~~Looking at the left hand side ~~~~~~~~~~~~~~~~~~~~~

Consider: #2 (1-2x)/3" " ->" " 2+(1-2x)/3" " ->" "color(green)( 6/3+(1-2x)/3)#

Consider:#" "-2x" "->" "color(green)((-6x)/3)#

So the left hand side becomes
#6/3+(1-2x)/3-(6x)/3 #

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

#color(green)((7-8x)/3)#

'~~~~~~~~~~Looking at the right hand side ~~~~~~~~~~~~~~~~~~~~~

Using the same method as above

Consider:#" "4 (2-3x)/3" " -> (12+2-3x)/3" " ->(14-3x)/3#

Consider:#" "-2/5# The denominator is not 3

So all the RHS is

#" "-2/5+(14-3x)/3" " -> (-6+70-15x)/15" ->color(green)( (63-15x)/15)#

'~~~~~~~~~~Putting both sides together~~~~~~~~~~~~~~~~~~~~

#color(green)((7-8x)/3)= color(green)( (63-15x)/15)#

Making the denominators the same gives

#(35-40x)/15=(63-15x)/15#

Thus:

#35-40x=63-15x#

#40x-15x=35-63#

#25x=-28#

#x=-28/25 -> -1 3/25#