## Algebra: A Combined Approach (4th Edition)

$x=3$
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, $x=3$