Answer
$x=3$
Work Step by Step
Step 1: Let us denote the unknown number by x.
Step 2: Five times the reciprocal of the unknown number = $5\times\frac{1}{x}=\frac{5}{x}$.
Step 3: $\frac{3}{2}$ the reciprocal of the number = $\frac{3}{2}\times\frac{1}{x}=\frac{3}{2x}$.
Step 4: According to the question, $\frac{5}{x}$=$\frac{3}{2x}+ \frac{7}{6}$.
Step 5: $\frac{3}{2x} - \frac{5}{x} = -\frac{7}{6}$.
Step 6: $\frac{3}{2x} - \frac{5\times2}{x\times2} = -\frac{7}{6}$
Step 7: $\frac{3-10}{2x}= -\frac{7}{6}$
Step 8: $\frac{-7}{2x}= -\frac{7}{6}$
Step 9: $\frac{1}{2x}= \frac{1}{6}$
Step 10: $x=\frac{6}{2}$
Step 11: Therefore, $x=3$
