Given: #-2(x-4)=2#
#color(magenta)("~~~~~~~~~~ Short Cut Method ~~~~~~~~~~")#
Jumping steps by doing some of it in my head!
#-2x-8=2#
#2x=6#
#x=3#
#color(magenta)("~~~~~~First Principle Method With Extensive explanation~~~~~~~~~~")#
I am choosing to rewrite it like this:
#-1xx2xx(x-2)=2 ...........................Equation (1)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Consider just the "2xx(x-4)#
This is the same as 2 of #(x-4)#
Which is #color(green)((x-4)+(x-4)->)color(magenta)( x+x-4-4)#
So #2(x-4)-> 2x-8#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Putting this back into #Equation (1)# gives:
#-1xx(2x-8)=2#
#color(brown)("Multiplying the bracket by -1 changes the sign of everything inside the bracket")#
#color(brown)(-2x+8=2)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("'Getting rid' of the 8 on the left hand side")#
Subtract #color(blue)(8)# from both sides.
#color(brown)(-2x+8 color(blue)(-8)=2color(blue)(-8))#
#-2x+0=-6#
Multiply both sides by -1 changing all the signs
#2x=6#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("'Getting rid' of the 2 in "2x)#
Divide both sides by 2. This is the same as #color(blue)(xx1/2)#
#color(brown)(2x color(blue)(xx1/2)=-6color(blue)(xx1/2)) #
#2/2 x = -6/2#
But #2/2 = 1# giving:
#x=-3#
