Subtract 9 from both sides of the inequality: $\displaystyle{3}{\left|{m}-{7}\right|}<{21}\usepackage{cmbright}\Huge\$

Divide both sides by 3: $\displaystyle{\left|{m}-{7}\right|}<{7}\usepackage{cmbright}\Huge\$

Rewrite without absolute value: $\displaystyle-{7}<{m}-{7}<{7}\usepackage{cmbright}\Huge\$

Add 7 to all 3 parts: $\displaystyle{0}<{m}<{14}\usepackage{cmbright}\Huge\$