Question

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

Answer 1

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`