How do you solve #-5k-19=5-13k#?
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You have to get all the variables on one side of the equation and all the numbers on the other.
The correct way to 'move' a term, is to add on its inverse to both sides.
The short cut is to put it on the other side and change the sign.
#-5k - 19 color(red)(+ 19) color(blue)(+ 13k) = 5 - 13k color(blue)( + 13k) color(red)(+ 19 ) #
The nett effect of this is:
#-5k cancel(- 19 color(red)(+ 19)) color(blue)(+ 13k) = 5 cancel(- 13k color(blue)( + 13k)) color(red)(+ 19 ) #
#-5k + 13k = 5 + 19#
# 8k = 24 " "# divide both sides by 3.
#k = 3#
The short method would look like this:
#-5k color(red)(- 19) = 5 color(blue)( - 13k) color(red)#
#-5k color(blue)( +13k) = 5 color(red)(+ 19)#
# 8k = 24 " "# divide both sides by 3.
#k = 3#
