How do you solve the inequality #-5/6d+8>13#?

1 Answer
Jan 31, 2016

Answer:

#d<-6#

Explanation:

We start off with #(-5)/6d+8>13#.
My goal is to isolate #d# on one side of the expression. My first step would be to subtract #8# on both sides, making the expression now #(-5)/6d>5#.

Now, I want to get #d# alone, so I would divide by #(-5)/6# on both sides, making the expression now show #d<(5)/(-5/6)#, which can be rewritten as #d<5*(-6/5)#. The #-5*(-6/5)#will divide out (like so:#cancel(5)*(-6/cancel(5))#), leaving #d<-6#.

Please note that the sign changed when I divided #(-5)/6# on both sides. This is because when I multiply or divide by a negative number, the sign of the expression changes, from #<# to #># or vice versa.