How do you solve the compound inequality #-20≤-6m-2≤58# and graph its solution?

1 Answer
Apr 22, 2015

Break up the given compound inequality # -20<=-6m-2<=58# into two separate inequalities and treat each separately (before recombining for their intersection).

Inequality 1:
#-20<= -6m-2#

#rarr 6m+2 <= 20#

#rarr m<= 3#

inequality 2:
-6m-2<= 58#

#rarr 6m+2 >= -58#

#rarr m>= -10#

Synthesis:
#m epsilon [-10,+3]#

Graph Solution:
This is somewhat more problematic since we don't really have an equation to graph. I suppose you could draw a number line and indicate the range along it...
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or identify #m# with values along the Y-axis and draw a band of values showing that those values apply for all values of #x#.