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Question Number 182093 by Fridunatjan08 last updated on 04/Dec/22

Solve the equation:  ((x−6)/(2020))+((x−5)/(2021))+((x−4)/(2022))=3

$${Solve}\:{the}\:{equation}: \\ $$$$\frac{{x}−\mathrm{6}}{\mathrm{2020}}+\frac{{x}−\mathrm{5}}{\mathrm{2021}}+\frac{{x}−\mathrm{4}}{\mathrm{2022}}=\mathrm{3} \\ $$

Commented by Fridunatjan08 last updated on 04/Dec/22

Please show me the easy way to solve this equation

$${Please}\:{show}\:{me}\:{the}\:{easy}\:{way}\:{to}\:{solve}\:{this}\:{equation} \\ $$

Commented by CElcedricjunior last updated on 04/Dec/22

x=2026  car  ((2026−6)/(2020))+((2026−5)/(2021))+((2026−4)/(2022))=((2020)/(2020))+((2021)/(2021))+((2022)/(2022))=1+1+1=3

$$\boldsymbol{{x}}=\mathrm{2026} \\ $$$$\boldsymbol{{car}} \\ $$$$\frac{\mathrm{2026}−\mathrm{6}}{\mathrm{2020}}+\frac{\mathrm{2026}−\mathrm{5}}{\mathrm{2021}}+\frac{\mathrm{2026}−\mathrm{4}}{\mathrm{2022}}=\frac{\mathrm{2020}}{\mathrm{2020}}+\frac{\mathrm{2021}}{\mathrm{2021}}+\frac{\mathrm{2022}}{\mathrm{2022}}=\mathrm{1}+\mathrm{1}+\mathrm{1}=\mathrm{3} \\ $$

Answered by Rasheed.Sindhi last updated on 04/Dec/22

The most tricky way  ((x−6)/(2020))+((x−5)/(2021))+((x−4)/(2022))=3  ((x−6)/(2020))−1+((x−5)/(2021))−1+((x−4)/(2022))−1=0  ((x−2026)/(2020))+((x−2026)/(2021))+((x−2026)/(2022))=0  (x−2026)((1/(2020))+(1/(2021))+(1/(2022)))=0  x−2026=0  x=2026

$$\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{most}}\:\boldsymbol{\mathrm{tricky}}\:\boldsymbol{\mathrm{way}} \\ $$$$\frac{{x}−\mathrm{6}}{\mathrm{2020}}+\frac{{x}−\mathrm{5}}{\mathrm{2021}}+\frac{{x}−\mathrm{4}}{\mathrm{2022}}=\mathrm{3} \\ $$$$\frac{{x}−\mathrm{6}}{\mathrm{2020}}−\mathrm{1}+\frac{{x}−\mathrm{5}}{\mathrm{2021}}−\mathrm{1}+\frac{{x}−\mathrm{4}}{\mathrm{2022}}−\mathrm{1}=\mathrm{0} \\ $$$$\frac{{x}−\mathrm{2026}}{\mathrm{2020}}+\frac{{x}−\mathrm{2026}}{\mathrm{2021}}+\frac{{x}−\mathrm{2026}}{\mathrm{2022}}=\mathrm{0} \\ $$$$\left({x}−\mathrm{2026}\right)\left(\frac{\mathrm{1}}{\mathrm{2020}}+\frac{\mathrm{1}}{\mathrm{2021}}+\frac{\mathrm{1}}{\mathrm{2022}}\right)=\mathrm{0} \\ $$$${x}−\mathrm{2026}=\mathrm{0} \\ $$$${x}=\mathrm{2026} \\ $$

Commented by Fridunatjan08 last updated on 04/Dec/22

thanks you!

$${thanks}\:{you}! \\ $$

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