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)#