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-5c-6<-c-3-4c
To find the opposite of c+3, find the opposite of each term.
-5c-6<-5c-3
Combine -c and -4c to get -5c.
-5c-6+5c<-3
Add 5c to both sides.
-6<-3
Combine -5c and 5c to get 0.
c\in \mathrm{R}
This is true for any c.