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Select the TWO expressions that are equivalent to the given expression.

(2x+2)−(3x+11)


(1 point)
Responses

−x+13
negative x plus 13

2x−3x+2+11
2 x minus 3 x plus 2 plus 11

−x−9
negative x minus 9

5x+13
5 x plus 13

2x−3x+2−11
2 x minus 3 x plus 2 minus 11

−x+9
negative x plus 9

5x+9
5 x plus 9

1 answer

To find the equivalent expressions for \((2x + 2) - (3x + 11)\), we start by simplifying the given expression:

  1. Distribute the negative sign to the second group: \[ (2x + 2) - (3x + 11) = 2x + 2 - 3x - 11 \]

  2. Combine like terms: \[ 2x - 3x + 2 - 11 = -x - 9 \]

Now, let's evaluate the given responses to see which ones are equivalent to \(-x - 9\):

  1. −x + 13: This is not equivalent.
  2. 2x − 3x + 2 + 11: This simplifies to: \[ 2x - 3x + 13 = -x + 13, \text{ which is not equivalent.} \]
  3. −x − 9: This is equivalent to the result we calculated.
  4. 5x + 13: This is not equivalent.
  5. 2x − 3x + 2 − 11: This simplifies to: \[ 2x - 3x + 2 - 11 = -x - 9, \text{ which is equivalent.} \]
  6. −x + 9: This is not equivalent.
  7. 5x + 9: This is not equivalent.

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

  1. −x − 9
  2. 2x − 3x + 2 − 11

Therefore, the correct responses are:

  • −x − 9
  • 2x − 3x + 2 − 11