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8-18-2-7-5-2-x-14-find-x-




Question Number 207247 by hardmath last updated on 10/May/24
8  +  ((18)/(2  +  (7/(5  +  (2/x)))))   =   14     find:   x = ?
$$\mathrm{8}\:\:+\:\:\frac{\mathrm{18}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{7}}{\mathrm{5}\:\:+\:\:\frac{\mathrm{2}}{\boldsymbol{\mathrm{x}}}}}\:\:\:=\:\:\:\mathrm{14}\:\:\:\:\:\mathrm{find}:\:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$
Commented by Frix last updated on 10/May/24
x=1
$${x}=\mathrm{1} \\ $$
Answered by Rasheed.Sindhi last updated on 11/May/24
8  +  ((18)/(2  +  (7/(5  +  (2/x)))))   =   14     find:   x = ?  ⇒  ((18)/(2  +  (7/(5  +  (2/x)))))   =   6     ⇒  (3/(2  +  (7/(  ((5x+2)/x)))))   =   1      ⇒  (3/(2  +  ((7x)/(  5x+2))))   =   1      ⇒(3/((10x+4+7x)/(5x+2)))=1  ⇒((3(5x+2))/(17x+4))=1  ⇒15x+6=17x+4  ⇒2x=2⇒x=1
$$\mathrm{8}\:\:+\:\:\frac{\mathrm{18}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{7}}{\mathrm{5}\:\:+\:\:\frac{\mathrm{2}}{\boldsymbol{\mathrm{x}}}}}\:\:\:=\:\:\:\mathrm{14}\:\:\:\:\:\mathrm{find}:\:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$$$\Rightarrow\:\:\frac{\mathrm{18}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{7}}{\mathrm{5}\:\:+\:\:\frac{\mathrm{2}}{\boldsymbol{\mathrm{x}}}}}\:\:\:=\:\:\:\mathrm{6}\:\:\: \\ $$$$\Rightarrow\:\:\frac{\mathrm{3}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{7}}{\:\:\frac{\mathrm{5}{x}+\mathrm{2}}{\boldsymbol{\mathrm{x}}}}}\:\:\:=\:\:\:\mathrm{1}\:\:\:\: \\ $$$$\Rightarrow\:\:\frac{\mathrm{3}}{\mathrm{2}\:\:+\:\:\frac{\mathrm{7}{x}}{\:\:\mathrm{5}{x}+\mathrm{2}}}\:\:\:=\:\:\:\mathrm{1}\:\:\:\: \\ $$$$\Rightarrow\frac{\mathrm{3}}{\frac{\mathrm{10}{x}+\mathrm{4}+\mathrm{7}{x}}{\mathrm{5}{x}+\mathrm{2}}}=\mathrm{1} \\ $$$$\Rightarrow\frac{\mathrm{3}\left(\mathrm{5}{x}+\mathrm{2}\right)}{\mathrm{17}{x}+\mathrm{4}}=\mathrm{1} \\ $$$$\Rightarrow\mathrm{15}{x}+\mathrm{6}=\mathrm{17}{x}+\mathrm{4} \\ $$$$\Rightarrow\mathrm{2}{x}=\mathrm{2}\Rightarrow{x}=\mathrm{1} \\ $$

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