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x-x-4-12-2x-7-x-




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

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