The trick with these is to rigidly stick to the rule that
color(red)("what you do to one side of the equation you do to the other.")
color(green)("The short cuts use this rule but they miss out stages.")
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Using first principles")
Given:" "color(brown)(9x+3=3x+27)
Subtract color(blue)(3) from both sides
color(brown)(9x+3color(blue)(-3)" "=" "3x+27color(blue)(-3))
color(brown)(9x+0" "=" "3x+24)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Subtract color(blue)(3x) from both sides
color(brown)(9xcolor(blue)(-3x)" "=" "3xcolor(blue)(-3x)+24)
color(brown)(6x" "=" "0+24)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Divide both sides by color(blue)(6)
color(brown)(6/(color(blue)(6))x" "=" "24/(color(blue)(6)))
But 6/6=1" and "24/6=4
1xx x=4
But the correct way to write 1xx x" is just "x" on its own"
x=4
