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
