Question

What is x+4/5=2/3- x-3/6

Answer 1

`x+(4)/(5)=(2)/(3)-x-(\\ot3^1)/(\\ot6_2)\\\\x+(4)/(5)=(2)/(3)-x-(1)/(2)\\\\find\ LCD((4)/(5);\ (2)/(3);\ (1)/(2))=2*3*5=30\\\\multiply\ both\ sides\ by\ LCD=30\\\\30x+30\cdot(4)/(5)=30\cdot(2)/(3)-30x-30\cdot(1)/(2)\\\\30x+6\cdot4=10\cdot2-30x-15\cdot1\\\\30x+24=20-30x-15`


`30x+24=5-30x\ \ \ \ |subtract\ 24\ from\ both\ sides\\\\30x=-19-30x\ \ \ \ \ |add\ 30x\ to\ both\ sides\\\\60x=-19\ \ \ \ \ |divide\ both\ sides\ by\ 60\\\\\boxed{x=-(19)/(60)}`




`(x+4)/(5)=(2)/(3)-(x-3)/(6)\\\\(x+4)/(5)=(2\cdot2)/(3\cdot2)-(x-3)/(6)\\\\(x+4)/(5)=(4)/(6)-(x-3)/(6)\\\\(x+4)/(5)=(4-(x-3))/(6)\\\\(x+4)/(5)=(4-x+3)/(6)\\\\(x+4)/(5)=(7-x)/(6)\ \ \ \ |cross\ multiply`


`6(x+4)=5(7-x)\\\\6(x)+6(4)=5(7)-5(x)\\\\6x+24=35-5x\ \ \ \ \ |subtract\ 24\ from\ both\ sides\\\\6x=11-5x\ \ \ \ \ |add\ 5x\ to\ both\ sides\\\\11x=11\ \ \ \ \ |divide\ both\ sides\ by\ 11\\\\\boxed{x=1}`