Question

How do you solve `x+ \frac { 3} { 8} = \frac { 7} { 5} x + \frac { 1} { 9} + \frac { 5} { 8}`?

Answer 1

`x=-65/72`

Explanation:

`x+3/8=7/5x+1/9+5/8`
to remove all denominators
Take LCM(8,5,9) and multiply with whole equation
`LCM(8,5,9)=360`

multiply equation by 360

`360x+3/8(360)=7/5(360)x+1/9(360)+5/8(360)`

`360x+3(45)=7(72)x+1(40)+5(45)`
`360x+135=504x+40+225`

Bring all terms of x one side

`504x-360x=135-40-225=135-265=-130`
`144x=-130`
`x=-130/144=-65/72`

Answer 2

`color(magenta)(x=-65/72`

Explanation:

`x+3/8=7/5x+1/9+5/8`

`:.x-7/5x=1/9+5/8-3/8`

`:.5/5x-7/5x=1/9+2/8`

`:.-2/5x=1/9+1/4`

`:.(-72x=20+45)/180`

multiply both sides by`180`

`:.-72x=65`

`:.color(magenta)(x=-65/72=-0.902777777`

~~~~~~~~~~~~~~~~

check:-

substitute `x=-0.902777777`

`:.-0.902777777+0.375=1.4(-0.902777777)+0.111111111+0.625`

`:.color(magenta)(-0.52777777=-0.52777777`