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 $m < 5 1/5 " or " m <5.2$

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