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Martie is simplifying an algebraic expression as shown below. (2-x)-3(x-4) 2-x-3x+12 which of these describes a correct procedure to complete the simplification?

User JoonT
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Final answer:

Martie correctly distributed the negative sign and the -3 in the expression (2-x)-3(x-4), resulting in 2 - x - 3x + 12. To complete the simplification, she should combine like terms to get -4x + 14.

Step-by-step explanation:

The student is working on simplifying an algebraic expression. The provided expression is (2-x)-3(x-4). The first step in the simplification process is to distribute the negative sign and the -3 across the terms inside the parentheses, which has been done correctly to yield 2 - x - 3x + 12. Now, we combine like terms to eliminate terms wherever possible to simplify:

  • Combine the constant terms: 2 + 12 = 14.
  • Combine the ‘x’ terms: -x - 3x = -4x.

The expression simplifies to -4x + 14. This is the simplest form of the expression. To verify the simplification, we can check the answer to ensure it is reasonable by substituting values for x and comparing the result with the original expression.

User Joe Heyming
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