Don't like too many calculations involving decimals so lets get rid of them.
Multiply everything in both sides of the = by 100
#30z-3=-8z#
Add #color(red)(8z)# to both sides (moves it to the LHS)
#color(green)(30z-3=-8z color(white)("ddd")->color(white)("ddd")30zcolor(red)(+8z)-3=-8z color(red)(+8z) )#
#color(white)("dddddddddddd.ddd")->color(white)("ddddd")color(green)(38zcolor(white)("d.")-3=color(white)("dddd")0)#
Add #color(red)(3)# to both sides (moves it to the RHS)
#color(green)(38z-3=0color(white)("dddddd") ->color(white)("ddd")38z-3 color(red)(+3)color(white)("d") =color(white)("d")0color(red)(+3)#
#color(white)("ddddddddddddddd")color(green)(->color(white)("dd.d")38zcolor(white)("d")+0color(white)("dd.")=color(white)("d")3#
Multiply both sides by #color(red)(1/38)# (moves the 38 to the RHS)
#color(green)(38zcolor(white)("d")=color(white)("dd")3color(white)("dddddd")->color(white)("dddd")30/color(red)(38) zcolor(white)("d")=color(white)("d")3/color(red)(38)#
But #38/38# is the same as 1 and #1xxz# is just #z#
#color(green)(color(white)("dddddddddddsddd")->color(white)("ddd")z=3/38#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Check")#
#0.3(3/38)-0.03=-0.08(3/38)#
By calculator #LHS ("left hand side") =RHS ("right hand side")#
