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select the two expressions that are equivalent to the given expression

(2x + 2) - (3x + 11)

answer choices

-x + 9

2x - 3x + 2 - 11

5x + 9

2x - 3x + 2 + 11

-x + 13

5x + 13

-x - 9

1 answer

To solve the expression \((2x + 2) - (3x + 11)\), we can simplify it step by step:

  1. Distribute the negative sign through the second set of parentheses: \[ (2x + 2) - (3x + 11) = 2x + 2 - 3x - 11 \]

  2. Combine like terms:

    • For the \(x\) terms: \(2x - 3x = -x\)
    • For the constant terms: \(2 - 11 = -9\)

So, the expression simplifies to: \[ -x - 9 \]

Now let's check which of the answer choices match the simplified expression.

  • Answer choice -x + 9: not equivalent
  • Answer choice 2x - 3x + 2 - 11: simplifies to \(-x - 9\) (equivalent)
  • Answer choice 5x + 9: not equivalent
  • Answer choice 2x - 3x + 2 + 11: simplifies to \(-x + 13\) (not equivalent)
  • Answer choice -x + 13: not equivalent
  • Answer choice 5x + 13: not equivalent
  • Answer choice -x - 9: equivalent (matches)

The two expressions that are equivalent to the given expression \((2x + 2) - (3x + 11)\) are:

  • 2x - 3x + 2 - 11
  • -x - 9