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)#