Let's simplify the expression:

\[
-2.9 + 2.1c + 3.8 - 0.82c
\]

### Step 1: Combine like terms.

- Combine the constants: \( -2.9 + 3.8 \)
- Combine the terms with \( c \): \( 2.1c - 0.82c \)

### Simplifying:

- Constants: \( -2.9 + 3.8 = 0.9 \)
- Variables: \( 2.1c - 0.82c = 1.28c \)

So, the simplified expression is:

\[
0.9 + 1.28c
\]

Would you like more details on how I combined the terms?

Here are 5 questions to explore further:
1. How do you simplify expressions with both constants and variables?
2. What are the rules for adding and subtracting decimals?
3. How do coefficients affect variables in an algebraic expression?
4. Why is it important to combine like terms in algebra?
5. Can you explain how positive and negative signs impact algebraic simplification?

**Tip:** When dealing with decimals, it helps to line up the decimal points to ensure accurate addition or subtraction.

Learn how to simplify the algebraic expression -2.9 + 2.1c + 3.8 - 0.82c step-by-step. This problem involves combining constants and variables, covering key algebraic concepts. Suitable for students in Grades 7-9.

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