Math Problem Statement

Which expression is equivalent to 2x + 3x + 6 − 122x + 3x + 6 − 12?

Select TWO correct answers.

A.5x − 65x − 6

B.5x + 6 − 125x + 6 − 12

C.5x + 65x + 6

D.5x − 125x − 12

E.x − 6x − 6

Solution

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

The original expression is:
2x+3x+6122x + 3x + 6 - 12

Step 1: Combine like terms

  • 2x+3x=5x2x + 3x = 5x
  • 612=66 - 12 = -6

Thus, the simplified form is: 5x65x - 6

Now let's compare with the given answer choices.

  • A. 5x65x - 6: This is correct!
  • B. 5x+6125x + 6 - 12: This simplifies to 5x65x - 6, so this is also correct!
  • C. 5x+65x + 6: This is incorrect.
  • D. 5x125x - 12: This is incorrect.
  • E. x6x - 6: This is incorrect.

Correct Answers:

  • A. 5x65x - 6
  • B. 5x+6125x + 6 - 12

Would you like any further clarifications?


Here are five follow-up questions:

  1. What are like terms, and how do you combine them?
  2. Can you explain the difference between positive and negative constants in simplification?
  3. How do parentheses change the way terms are combined?
  4. How can this knowledge help solve algebraic equations?
  5. How would the process change if variables had exponents?

Tip: Always double-check for arithmetic or sign errors when simplifying expressions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplification of Expressions
Combining Like Terms

Formulas

2x + 3x = 5x
6 - 12 = -6

Theorems

Properties of Addition and Subtraction
Distributive Property (implicitly used in combining constants)

Suitable Grade Level

Grades 6-8