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Question

Difficulty: EasySimplifying Algebraic Expressions

Which of the following is the simplified form of the expression 4(2x−3)+5x4(2x - 3) + 5x?

  1. 13x−1213x - 12Answer
  2. B
    13x−313x - 3
  3. C
    xx
  4. D
    13x+1213x + 12

Answer

13x−1213x - 12
The correct answer is obtained by first applying the distributive property to multiply 44 by both 2x2x and −3-3, yielding 8x−128x - 12. Then, the like terms 8x8x and 5x5x are combined to get 13x13x. The constant −12-12 cannot be combined with the variable terms, so the fully simplified expression is 13x−1213x - 12.

Step-by-Step Solution

1
Distribute the 4 into the parentheses.
8x−12+5x8x - 12 + 5x
The distributive property requires multiplying the constant outside the parentheses by each term inside.
2
Group and combine the like terms.
13x−1213x - 12
The terms 8x8x and 5x5x are like terms and can be added together. The constant −12-12 cannot be combined with variable terms.

Key Concept

Simplifying Algebraic Expressions via Distribution and Combining Like Terms
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Topics

Simplifying Algebraic Expressions

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