Let's simplify the given expression step by step:

The expression is:

\[
2(-4x) + 5(2y) - x
\]

1. Distribute the constants inside the parentheses:
   \[
   2(-4x) = -8x
   \]
   \[
   5(2y) = 10y
   \]

Now the expression becomes:

\[
-8x + 10y - x
\]

2. Combine like terms:
   \[
   -8x - x = -9x
   \]

Thus, the simplified expression is:

\[
-9x + 10y
\]

Would you like more details or have any further questions?

Here are 5 questions to consider next:
1. How would the expression change if different values were substituted for \( x \) and \( y \)?
2. What if the sign of one of the terms were different, how would that affect the outcome?
3. How would this expression look if both \( x \) and \( y \) were positive integers?
4. Can this expression be factored further?
5. What happens when you add another variable term to the expression?

**Tip:** Always combine like terms (same variables raised to the same power) to simplify algebraic expressions efficiently.

Learn how to simplify the algebraic expression 2(-4x) + 5(2y) - x step by step. This problem involves using the distributive property and combining like terms. Ideal for students in Grades 6-8 looking to understand basic algebraic simplification techniques.

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