How do you solve x+ \frac { 3} { 8} = \frac { 7} { 5} x + \frac { 1} { 9} + \frac { 5} { 8}x+38=75x+19+58?

2 Answers
Sep 22, 2017

x=-65/72x=6572

Explanation:

x+3/8=7/5x+1/9+5/8x+38=75x+19+58
to remove all denominators
Take LCM(8,5,9) and multiply with whole equation
LCM(8,5,9)=360LCM(8,5,9)=360

multiply equation by 360

360x+3/8(360)=7/5(360)x+1/9(360)+5/8(360)360x+38(360)=75(360)x+19(360)+58(360)

360x+3(45)=7(72)x+1(40)+5(45)360x+3(45)=7(72)x+1(40)+5(45)
360x+135=504x+40+225360x+135=504x+40+225

Bring all terms of x one side

504x-360x=135-40-225=135-265=-130504x360x=13540225=135265=130
144x=-130144x=130
x=-130/144=-65/72x=130144=6572

Sep 22, 2017

color(magenta)(x=-65/72x=6572

Explanation:

x+3/8=7/5x+1/9+5/8x+38=75x+19+58

:.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