Question

How do I solve `1/3(x-2)-3x=16/3-2(x-1)`?

Answer 1

`x=-12`

Explanation:

If you have an equation which has fractions, you can get rid of the denominators by multiplying by the `LCD`. (`3` in this case)

Multiply each term by `3` and cancel the denominators.

`color(blue)(cancel3xx)1/cancel3(x-2)-color(blue)(3xx)3x= color(blue)(cancel3xx)16/cancel3 -color(blue)(3xx)2(x-1)`

This gives an equation without any fractions.

`color(white)(xxxx)(x-2) -9x = 16-6(x-1)" "larr` simplify

`color(white)(xxxxx)x-2 -9x =16-6x color(red)( +6)larr` watch the sign!

`color(white)(xxxxx)-8x+6x =22+2" "larr` rearrange the terms

`color(white)(xxxxxxxxx)-2x = 24`

`color(white)(xxxxxxxxxx.x)x = -12`