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

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(1) Answers

Bucholtz970

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