Let's solve the equation step by step:

Given:

\[
8.5 = 6.5(2d - 3) + d
\]

### Step 1: Expand the equation
Distribute \(6.5\) across \((2d - 3)\):

\[
8.5 = 6.5 \times 2d - 6.5 \times 3 + d
\]
\[
8.5 = 13d - 19.5 + d
\]

### Step 2: Combine like terms
Combine \(13d\) and \(d\):

\[
8.5 = 14d - 19.5
\]

### Step 3: Isolate \(d\)
Add \(19.5\) to both sides of the equation:

\[
8.5 + 19.5 = 14d
\]
\[
28 = 14d
\]

### Step 4: Solve for \(d\)
Divide both sides by \(14\):

\[
d = \frac{28}{14} = 2
\]

### Solution:
\[
d = 2
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you solve equations with variables on both sides?
2. What happens when equations involve fractions?
3. How do you check if your solution to an equation is correct?
4. How do you solve multi-step equations in algebra?
5. What methods can you use to simplify complex algebraic expressions?

**Tip:** Always distribute and combine like terms carefully to avoid mistakes when solving equations.

Learn how to solve the linear equation 8.5 = 6.5(2d - 3) + d with a detailed, step-by-step explanation. This problem covers key algebraic concepts such as the distributive property and combining like terms, suitable for students in Grades 7-8.

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