Simplify the expression -2..5(x-3) - 7(4-8.5x)

Let's simplify the given expression step-by-step:

The expression is:

\[
-2.5(x - 3) - 7(4 - 8.5x)
\]

### Step 1: Distribute the terms inside the parentheses

Distribute \(-2.5\) and \(-7\) to each term inside their respective parentheses:

\[
-2.5 \cdot x - 2.5 \cdot (-3) - 7 \cdot 4 - 7 \cdot (-8.5x)
\]

Simplify each multiplication:

\[
-2.5x + 7 - 28 + 59.5x
\]

### Step 2: Combine like terms

Combine the \(x\) terms and the constant terms:

\[
(-2.5x + 59.5x) + (7 - 28)
\]

Simplify each group:

\[
57x - 21
\]

### Final Simplified Expression

\[
\boxed{57x - 21}
\]

Would you like more details, or do you have any questions? Here are some related questions to explore further:

1. How would the simplification change if the coefficients were different?
2. How can you factor the resulting expression?
3. What if you had to evaluate this expression for a specific value of \(x\)?
4. How would adding more terms affect the simplification process?
5. What techniques are useful for checking your work in simplification?

**Tip:** Always distribute negative signs carefully to avoid errors during simplification!

Learn how to simplify the expression -2.5(x - 3) - 7(4 - 8.5x) with a detailed step-by-step solution. This problem covers key algebraic concepts, including the distributive property and combining like terms. Suitable for high school students.

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