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solve-for-x-1-2-x-6-11-

Question Number 456 by Karting7442 last updated on 25/Jan/15 $${solve}\:{for}\:{x}:\:\:\frac{\mathrm{1}}{\mathrm{2}}{x}+\mathrm{6}=\mathrm{11} \\ $$$$ \\ $$ Answered by prakash jain last updated on 09/Jan/15 $$\frac{\mathrm{1}}{\mathrm{2}}{x}+\mathrm{6}=\mathrm{11} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}{x}=\mathrm{11}−\mathrm{6}…

x-1-3-1-1-4-2-1-5-3-1-1002-1000-x-1000-

Question Number 65992 by naka3546 last updated on 07/Aug/19 $${x}\:\:=\:\:\frac{\mathrm{1}}{\mathrm{3}\centerdot\mathrm{1}!}\:+\:\frac{\mathrm{1}}{\mathrm{4}\centerdot\mathrm{2}!}\:+\:\frac{\mathrm{1}}{\mathrm{5}\centerdot\mathrm{3}!}\:+\:\ldots\:+\:\frac{\mathrm{1}}{\mathrm{1002}\centerdot\mathrm{1000}!} \\ $$$${x}\centerdot\mathrm{1000}!\:\:=\:\:? \\ $$ Commented by Prithwish sen last updated on 08/Aug/19 $$\mathrm{last}\:\mathrm{term}\:\frac{\mathrm{n}}{\left(\mathrm{n}+\mathrm{1}\right)!}\:\:\mathrm{where}\:\mathrm{n}=\:\mathrm{1001} \\ $$$$\therefore\:\left[\frac{\mathrm{n}+\mathrm{1}−\mathrm{1}}{\left(\mathrm{n}+\mathrm{1}\right)!}\right]\:=\:\frac{\mathrm{1}}{\mathrm{n}!}\:−\:\frac{\mathrm{1}}{\left(\mathrm{n}+\mathrm{1}\right)!}…

solve-for-x-3-14x-15-72-

Question Number 453 by Karting7442 last updated on 25/Jan/15 $${solve}\:{for}\:{x}\:\:\:\mathrm{3}\left(\mathrm{14}{x}−\mathrm{15}\right)=−\mathrm{72} \\ $$ Answered by prakash jain last updated on 09/Jan/15 $$\mathrm{3}\left(\mathrm{14}{x}−\mathrm{15}\right)=−\mathrm{72} \\ $$$$\mathrm{42}{x}−\mathrm{45}=−\mathrm{72} \\ $$$$\mathrm{42}{x}=−\mathrm{72}+\mathrm{45}…