# How do you solve <mstyle displaystyle="true"> m </mrow>

How do you solve $\frac{m}{3}-3<\frac{4}{3}-\frac{m}{2}$ ?
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Step 1
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.
$\frac{6×m}{3}-6×3<\frac{6×4}{3}-\frac{6×m}{2}$
$\frac{{\overline{)6}}^{2}×m}{\overline{)3}}-6×3<\frac{{\overline{)6}}^{2}×4}{\overline{)3}}-\frac{{\overline{)6}}^{3}×m}{\overline{)2}}$
$\to 2m-18<8-3m\phantom{\rule{1ex}{0ex}}\text{}\phantom{\rule{1ex}{0ex}}←$ rearrange the terms
$2m+3m<8+18$
$5m<26$
$m<\frac{26}{5}$
This is the same as $m<5\frac{1}{5}\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}m<5.2$