How do you solve #\frac { 3x } { 5} - x = \frac { x } { 10} - \frac { 5} { 2}#?

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Answer 1 · 2017-04-09T15:18:55

#color(blue)(x=5#

#(3x)/5-x=x/10-5/2#

#:.(6x-10x=x-25)/10#

#:.(6x-10x-x=-25)/10#

#:.(-5x)/10=(-25)/10#

multiply L.H.S and R.H.S by #color(blue)(-10#

#:.(-cancel10^color(blue)1)/1 xx (-5x)/cancel10^color(blue)1=(-cancel10^color(blue)1)/1 xx (-25)/cancel10^color(blue)1#

#:.5x=25#

#:.color(blue)(x=5#

substitute# x=5#

#:.(3(color(blue)5))/5-color(blue)5=cancelcolor(blue)5^color(blue)1/cancel10^color(blue)2-5/2#

#:.15/5-5=1/2-5/2#

#:.15/5-25/5=-4/2#

#:.-10/5=-2#

#:.-2=-2#