How do you solve and graph #m-2< -8# or #m/8>1#?

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Answer 1 · 2018-06-29T03:57:41

#m<-6 or m>8# or in interval notation #m in (-oo,-6) uu (8,+oo)#

#m-2<-8 or m/8>1#

First consider: #m-2<-8#

Add 2 to both sides.

#-> m<-8+2#

#m<-6#

Next consider: #m/8>1#

Multiply both sides by 8.

#-> m>8#

Hence our compound inequality simplifies to: #m<-6 or m>8#
or in interval notation #m in (-oo,-6) uu (8,+oo)#

We can represent this graphically on a 2D plane where #m# is the horizontal axis, as below.

graph{(x+6)(-x+8)<0 [-14.24, 14.23, -7.12, 7.11]}

So, #m# may take all values on the horizontal axis in the shaded areas.