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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?

Let the number be x. Thus, the reciprocal is $\frac{1}{x}$. Three times x = 3x. Reciprocal of 3x = $\frac{1}{3x}$. Two times x = 2x. Reciprocal of 2x = $\frac{1}{2x}$ Given, $7 - \frac{1}{3x} = \frac{1}{2x}$ $\frac{1}{2x} + \frac{1}{3x} = 7$ $\frac{3 + 2}{6x} = 7$ 5 = 42x x = $\frac{5}{42}$ Thus, the number is $\frac{5}{42}$.