#color(blue)("Objective")#
To have a single #a# on one side of the = and everything else on the other side. This is mathematically saying that 'a is equal to ...' .
#color(blue)("Method")#
If some thing is on a side that you do not wish it to be 'remove' it.
For addition/subtraction you change it to 0. Any value that has 0 added or subtracted from it does not change.
For multiply/divide you change it to 1. Anything multiplied by 1 does not change its value
#color(blue)("Extremely important rule")#
#color(brown)("What yo do to one side of the = you do to the other side")#
#color(blue)("Applying the method and rule")#
Given: #color(white)(...)color(brown)(4a-4=8+a)#
To remove the #color(brown)(a)# from the right hand side we subtract a. That is: #color(blue)(-a)#:
RHS#-> color(brown)(8+a)color(blue)(-a)#
What we do to one side we do to the other:
#color(brown)(4a-4color(blue)(-a)=8+acolor(blue)(-a))#
but #color(brown)(+acolor(blue)(-a))=color(green)(0)color(white)(..)# giving:
#color(brown)(4acolor(blue)(-a) -4=8color(green)(+0))#
#color(brown)(3a-4=8)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
To 'get rid' of the -4 on the LHS add #color(blue)( 4)# #underline("to both sides")#
#color(brown)(3a-4color(blue)(+4)=8color(blue)(+4))#
but #color(brown)(-4color(blue)(+4)=color(green)(0))# giving:
#color(brown)(3a color(green)(+0) =12#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
To 'get rid' of the 3 in #3a# divide by #color(blue)(3)#
Not that #color(blue)(-: 3 color(brown)(" is the same as") xx 1/3)#
#color(brown)(3acolor(blue)(xx1/3)= 12color(blue)(xx1/3))#
#color(brown)(3/color(blue)(3)xx a =12/color(blue)(3))#
#a = 4#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(red)("Once you are confident about how to do this you will not only")#
#color(red)("get faster but be able to apply the shortcuts with confidence").#
#color(green)("This will make you even faster still!")#
