Question Number 94780 by Abdulrahman last updated on 20/May/20
$$\mathrm{x}!\left(\mathrm{x}−\mathrm{4}\right)!=\mathrm{12}\left(\mathrm{2x}−\mathrm{7}\right)! \\ $$$$\mathrm{x}=? \\ $$
Commented by MJS last updated on 21/May/20
$${x}\geqslant\mathrm{4} \\ $$$$\mathrm{trying} \\ $$$$\mathrm{4}!\mathrm{0}!>\mathrm{12}×\mathrm{1}! \\ $$$$\mathrm{5}!\mathrm{1}!>\mathrm{12}×\mathrm{3}! \\ $$$$\mathrm{6}!\mathrm{2}!=\mathrm{12}×\mathrm{5}! \\ $$$$\mathrm{7}!\mathrm{3}!<\mathrm{12}×\mathrm{7}! \\ $$$$\Rightarrow\:{x}=\mathrm{6} \\ $$