How do you solve #\frac { m } { 3} - 3< \frac { 4} { 3} - \frac { m } { 2}#?

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Answer 1 · 2017-09-01T13:14:19

#m < 26/5#

#m < 5 1/5#

#m <5.2#

You can get rid of the fractions straight away.

Multiply each term of the inequality by the #LCD#, which is #6#.

This will allow you to cancel the denominators and thereby get rid of the fractions altogether.

#(color(blue)(6xx)m)/3-color(blue)(6xx3) < (color(blue)(6xx)4)/3 - (color(blue)(6xxm))/2#

#(color(blue)(cancel6^2xx)m)/cancel3-color(blue)(6xx3) < (color(blue)(cancel6^2xx)4)/cancel3 - (color(blue)(cancel6^3xxm))/cancel2#

#rarr 2m-18 < 8-3m" "larr# rearrange the terms

#2m+3m <8+18#

#5m < 26#

#m < 26/5#

This is the same as #m < 5 1/5 " or " m <5.2#