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].
