Question

1. (\frac{6}{b - 1} = \frac{9}{7})

Explanation:

Step1: Cross - multiply the equation

Given the equation $\frac{6}{b - 1}=\frac{9}{7}$, cross - multiplying (which is based on the property of proportions: if $\frac{a}{c}=\frac{d}{e}$, then $a\times e = c\times d$) gives us $6\times7=9\times(b - 1)$.
Calculating the left - hand side: $6\times7 = 42$, and the right - hand side is $9(b - 1)=9b-9$. So the equation becomes $42 = 9b-9$.

Step2: Isolate the variable term

Add 9 to both sides of the equation $42 = 9b - 9$ to get the variable term by itself.
$42+9=9b-9 + 9$, which simplifies to $51 = 9b$.

Step3: Solve for b

Divide both sides of the equation $51 = 9b$ by 9. We can simplify the fraction $\frac{51}{9}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 3. So $\frac{51\div3}{9\div3}=\frac{17}{3}$. So $b=\frac{17}{3}$.

Answer:

$b = \frac{17}{3}$