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#
