If #-3/8 <= m/-2 + 8<=7#, what is a possible value of #4m-2#?

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Answer 1 · 2016-11-13T09:44:11

#6<=4m-2<=65#

First, you can subtract 8 from all members of the inequalities, to get:

#-3/8-8<=-m/2<=7-8#

#-67/8<=-m/2<=-1#

then you can multiply all the terms by -2 to eliminate the fraction, but in this case you must invert the inequality since -2 is a negative number:

#2<=m<=67/4#

Then you can multiply all the terms by 4 and subtract 2 to get:

#color(red)4*2color(red)(-2)<=color(red)4mcolor(red)(-2)<=cancelcolor(red)4*67/cancel4color(red)(-2)#

This gives the required expression in the middle.

#6<=4m-2<=65#