Solve for: (6)/(b-1)=(9)/(7)

Expression: $\frac{ 6 }{ b-1 }=\frac{ 9 }{ 7 }$

Determine the defined range

$\begin{array} { l }\frac{ 6 }{ b-1 }=\frac{ 9 }{ 7 },& b≠1\end{array}$

Simplify the equation using cross-multiplication

$42=9\left( b-1 \right)$

Distribute $9$ through the parentheses

$42=9b-9$

Move the variable to the left-hand side and change its sign

$42-9b=-9$

Move the constant to the right-hand side and change its sign

$-9b=-9-42$

Calculate the difference

$-9b=-51$

Divide both sides of the equation by $-9$

$\begin{array} { l }b=\frac{ 17 }{ 3 },& b≠1\end{array}$

Check if the solution is in the defined range

$\begin{align*}&b=\frac{ 17 }{ 3 } \\&\begin{array} { l }b=5 \frac{ 2 }{ 3 },& b=5.\overset{ \cdot }{ 6 } \end{array}\end{align*}$