Let's simplify the expression step by step:

The given expression is:

\[
2(-5d + 3d - 3) + \frac{7}{5d}
\]

### Step 1: Distribute the 2 into the parentheses
We distribute the 2 across the terms inside the parentheses:

\[
2(-5d + 3d - 3) = 2(-5d) + 2(3d) + 2(-3)
\]

Simplifying each term:

\[
2(-5d) = -10d, \quad 2(3d) = 6d, \quad 2(-3) = -6
\]

Thus, the expression becomes:

\[
-10d + 6d - 6 + \frac{7}{5d}
\]

### Step 2: Combine like terms
Now, combine the \(d\)-terms:

\[
-10d + 6d = -4d
\]

So the expression simplifies to:

\[
-4d - 6 + \frac{7}{5d}
\]

### Final Simplified Expression:

\[
-4d - 6 + \frac{7}{5d}
\]

This is the simplified version of the expression.

Would you like further details on this, or do you have any questions?

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Here are 5 related questions:
1. How would you handle this if it were an equation to solve for \(d\)?
2. How do you find the least common denominator for expressions involving fractions?
3. What happens if \(d = 0\) in this expression?
4. Can you express the result as a single fraction?
5. How do you handle simplifying more complex algebraic expressions?

**Tip**: Always double-check signs when distributing negative numbers in an expression to avoid errors.

Learn how to simplify the algebraic expression 2(-5d + 3d - 3) + 7/5d step by step. This solution covers key algebra concepts like distributing, combining like terms, and handling fractions. Suitable for students in Grades 8-10.

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