Let's solve the equation step by step:

The given equation is:

\[
6 + \frac{4}{5b} = \frac{9}{10b}
\]

### Step 1: Eliminate the denominators by multiplying both sides of the equation by the least common denominator (LCD).

The denominators are \( 5b \) and \( 10b \), and their least common denominator is \( 10b \). Multiply both sides of the equation by \( 10b \):

\[
10b \left( 6 + \frac{4}{5b} \right) = 10b \left( \frac{9}{10b} \right)
\]

### Step 2: Distribute and simplify.

Distribute \( 10b \) on the left side:

\[
10b \cdot 6 + 10b \cdot \frac{4}{5b} = 9
\]

Simplify each term:

\[
60b + 8 = 9
\]

### Step 3: Isolate the term with \( b \).

Subtract 8 from both sides:

\[
60b = 1
\]

### Step 4: Solve for \( b \).

Now divide both sides by 60:

\[
b = \frac{1}{60}
\]

So, the solution is:

\[
b = \frac{1}{60}
\]

Would you like more details or have any questions?

### Related Questions:
1. What happens if you change the coefficients in this equation?
2. How do you solve an equation with more complex denominators?
3. What does it mean when there's no solution to an equation?
4. How do you solve equations with variables in the denominator?
5. Can you generalize this approach for any fractions in an equation?

### Tip:
Always check your solution by substituting the value of \( b \) back into the original equation to ensure accuracy.

Master the step-by-step solution of the linear equation 6 + 4/5b = 9/10b, focusing on eliminating fractions using cross-multiplication. This guide is perfect for students in Grades 8-10 and covers key algebraic concepts like the distributive property.

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