Find an expression which represents the sum of left parenthesis, 10, x, minus, 2, right parenthesis(10*x*−2) and left parenthesis, minus, 6, x, minus, 9, right parenthesis(−6*x*−9) in simplest terms.

To find the expression representing the sum of \( (10x - 2) \) and \( (-6x - 9) \), follow these steps:

1. **Write down the original expressions:**
   \[
   (10x - 2) + (-6x - 9)
   \]

2. **Combine like terms:**

   - Combine the \(x\) terms: 
     \[
     10x + (-6x) = 4x
     \]
   
   - Combine the constant terms:
     \[
     -2 + (-9) = -11
     \]

3. **Write the simplified expression:**
   \[
   4x - 11
   \]

So, the expression that represents the sum in simplest terms is \( \boxed{4x - 11} \).

Would you like further explanation or examples? Here are some related questions:

1. How would the expression change if the second term was positive, \(6x + 9\)?
2. Can you factor the expression \(4x - 11\)?
3. What happens if \(x = 2\)? What is the value of the expression?
4. How does the expression relate to a linear equation?
5. What is the derivative of the expression \(4x - 11\) with respect to \(x\)?

**Tip:** When combining expressions, always pay close attention to the signs (positive or negative) in front of each term.

Learn how to simplify the expression (10x - 2) + (-6x - 9) step-by-step. Combine like terms and simplify to find the solution. Suitable for students in Grades 7-9 studying algebra and combining like terms.

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