Question

How do you solve `3/4x-4/9=7/18x-2/3`?

Answer 1

`x=color(green)(-8/13`

Explanation:

`3/4x-4/9=7/18x-2/3`

`:.(27x-16=14x-24)/color(green)36`

`:.(27x)/color(green)36-16/color(green)36=(14x)/color(green)36-24/color(green)36`

multiply L.H.S and R.H.S. by`color(green)(36`

`:.27x-16=14x-24`

`:.27x-14x=-24+16`

`13x=-8`

`:.color(green)(x=-8/13`

check:

substitute `color(green)(x=-8/13`

`:.3/4(color(green)(-8/13))-4/9=7/18(color(green)(-8/13))-2/3`

`:.-24/52-4/9=-56/234-2/3`

`:.(-108-104=-56-156)/color(green)234`

`:.-108/color(green)234-104/color(green)234=-56/color(green)234-156/color(green)234`

multiply L.H.S and R.H.S. by`color(green)234`

`:.-108-104=-56-156`

`:.-212=-212`