Math Problem Statement

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

Solution

To find the expression representing the sum of (10x2)(10x - 2) and (6x9)(-6x - 9), follow these steps:

  1. Write down the original expressions: (10x2)+(6x9)(10x - 2) + (-6x - 9)

  2. Combine like terms:

    • Combine the xx terms: 10x+(6x)=4x10x + (-6x) = 4x

    • Combine the constant terms: 2+(9)=11-2 + (-9) = -11

  3. Write the simplified expression: 4x114x - 11

So, the expression that represents the sum in simplest terms is 4x11\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+96x + 9?
  2. Can you factor the expression 4x114x - 11?
  3. What happens if x=2x = 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 4x114x - 11 with respect to xx?

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

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Math Problem Analysis

Mathematical Concepts

Algebra
Combining Like Terms

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9