#color(blue)("Shortcut method:")#
Take the 4 over to the other side of the equals and make its sign opposite to subtract (add)
#m/11=-6+4#
Writing #m/11# is another way of saying #m-:11#
Take the 11 over to the other side of the equals and make its sign opposite to divide (multiply)
#m=11xx(-6+4)#
#m=-22#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("First principle method - in detail:")#
The shortcut approach is just remembering the consequences of the first principle approach.
#m/11-4=-6#
First we isolate the term with #m# in it by 'getting rid' of the 4. We turn the 4 into 0. Any number plus 0 does change its value.
Add #color(red)(4)# to both sides
#color(green)(m/11-4color(white)("d")=color(white)("d")-6 color(white)("dddd")->color(white)("dddd")m/11color(white)("d")ubrace( -4 color(red)(+4)) color(white)("d")=color(white)("d")ubrace(-6color(red)(+4)))#
#color(white)("dddddddddddddddddddddddddddddd")darrcolor(white)("ddddddd.")darr#
#color(green)(color(white)("ddddddddddddddd.dd")->color(white)("dddd") m/11color(white)("d") +0color(white)("ddd")=color(white)("d")-2 )#
We now need to 'get rid' of the 11 from #m/11#. We do this by changing the 11 into 1. Note that 1 times anything does not change its value.
Multiply both sides by #color(red)(11)#
#color(green)(m/11color(white)("d")=color(white)("d")-2color(white)("dddddd")->color(white)("dddd")m/11 color(red)(xx11)color(white)("d")=color(white)("d")-2color(red)
(xx11))#
#color(green)(color(white)("ddddddddddddddddd")->color(white)("dddd")m xxcolor(red)(11)/11color(white)("d")=color(white)("d")-22 )#
#color(green)(color(white)("ddddddddddddddddd")->color(white)("dddd")mxxcolor(white)("d")1color(white)("d")=color(white)("d")-22#
#color(green)(m=-22)#
