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When the reciprocal of three times a number is subtracted from 7, the result is the reciprocal of twice the number. find the number?

Respuesta :

Let the number be x. Thus, the reciprocal is [tex] \frac{1}{x} [/tex].

Three times x = 3x. Reciprocal of 3x = [tex] \frac{1}{3x} [/tex].

Two times x = 2x. Reciprocal of 2x = [tex] \frac{1}{2x} [/tex]

Given,

[tex]7 - \frac{1}{3x} = \frac{1}{2x} [/tex]

[tex] \frac{1}{2x} + \frac{1}{3x} = 7[/tex]

[tex] \frac{3 + 2}{6x} = 7[/tex]

5 = 42x

x = [tex] \frac{5}{42} [/tex]

Thus, the number is [tex] \frac{5}{42} [/tex].

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