Objective: to end up with #x# on one side of the equals sign and everything else on the other side.
#color(blue)("Principles behind Simons' short cut method")#
Simon used the shortcut method. This is based on: if you move something to the other side of the = you reverse 'what it is doing';
So if you had say:#" " x+3=2# and you wished to move the #+3#
When you move the #+3# to the other side it becomes #-3#
'~~~~~~~~~~~
Suppose you had #x-:3=2# and you wished to move the #-:3# to the others side.
So #x-:3=2" becomes " x=2xx3#
Another way of writing #x-:3" is " x/3#
so #x/3=2" becomes " x=2xx3#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("The first principle method that the short cut method is based on")#
Given:#" " 12/5" "=" "x/6#
Write as: #color(brown)(" "12/5" "=" " x xx1/6)#
Multiply both sides by#" " color(blue)(6)# giving:
#" "color(brown)(12/5 color(blue)(xx6)" "=" "x xx 1/6color(blue)(xx6)#
#" "color(brown)((12color(blue)(xx6))/5" "=" "x xx(color(blue)(6))/6) #
But #6/6=1 # giving:
#" "72/5" "=" "x#
#72 -: 5 = 14 2/5 # so we have
#" "color(red)(x= 14 2/5)#
