How do you solve \frac { m } { 3} - 3< \frac { 4} { 3} - \frac { m } { 2}m33<43m2?

1 Answer
Sep 1, 2017

m < 26/5m<265

m < 5 1/5m<515

m <5.2m<5.2

Explanation:

You can get rid of the fractions straight away.

Multiply each term of the inequality by the LCDLCD, which is 66.

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))/26×m36×3<6×436×m2

(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