Given: #7.1=3.8+n#
Don't like decimals so lets get rid of them. Multiply everything on both sides by 10
#71=38+10 n#
As per convention put the unknown on the left. So turn everything round the other way
#10n+38=71 larr" Means exactly the same thing"#
Subtract #color(red)(38)# from both sides
#color(green)(10n+38=71 color(white)("ddd")->color(white)("ddd")10n+38color(red)(-38)color(white)("d")=color(white)("d")71color(red)(-38) )#
#color(green)(color(white)("ddddddddddddd.d")->color(white)("ddd")10n + color(white)("dd")0color(white)("ddd.")=color(white)("ddd")33)#
Divide both sides by #color(red)(10)#
#color(green)(10n=33color(white)("ddddddd")->color(white)("ddd")10/color(red)(10)ncolor(white)("d")=color(white)("d")33/color(red)(10) )#
But #10/10=1 and 1xxn = n# giving:
#color(green)(n=3.3)#
