Let's solve the equation step by step:

\[
0.75(8b + 4) - 1 = 4b + 14
\]

### Step 1: Distribute the 0.75 on the left-hand side.
\[
0.75 \times 8b + 0.75 \times 4 = 4b + 14
\]
\[
6b + 3 - 1 = 4b + 14
\]

### Step 2: Simplify the left-hand side.
\[
6b + 2 = 4b + 14
\]

### Step 3: Move the \(4b\) term from the right-hand side to the left-hand side by subtracting \(4b\) from both sides.
\[
6b - 4b + 2 = 14
\]
\[
2b + 2 = 14
\]

### Step 4: Subtract 2 from both sides to isolate the \(2b\) term.
\[
2b = 12
\]

### Step 5: Divide both sides by 2 to solve for \(b\).
\[
b = 6
\]

The solution is:
\[
b = 6
\]

Would you like further details or clarifications? 

Here are 5 related questions to deepen your understanding:
1. How can you solve equations with decimals?
2. What are the properties of equality used in solving linear equations?
3. Can you apply the distributive property with fractions?
4. How do you handle variables on both sides of an equation?
5. What happens if the variable's coefficient is negative?

**Tip:** When distributing a decimal or fraction, it's often easier to convert them into fractions or decimals first, if appropriate.

Explore how to solve the linear equation 0.75(8b+4)-1=4b+14 using the distributive property. This step-by-step solution covers essential algebraic concepts such as solving for variables, applying the distributive property, and managing terms on both sides. Perfect for students in Grades 7-9.

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