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

(2x+2)−(3x+11)

(2 points)
Responses

−x−9

−x+9

5x+13

2x−3x+2+11

5x+9

2x−3x+2−11

−x+13

1 answer

To simplify the expression \((2x + 2) - (3x + 11)\), we can follow these steps:

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

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

Now, we represent the simplified expression: \[ -x - 9 \]

Next, we check the given responses to find which are equivalent to \(-x - 9\):

  1. Response: \(-x - 9\): This is exactly the same, so it is equivalent.
  2. Response: \(-x + 9\): Not equivalent, as the signs are different.
  3. Response: \(5x + 13\): Not equivalent.
  4. Response: \(2x - 3x + 2 + 11\): This simplifies to \(-x + 13\), not equivalent.
  5. Response: \(5x + 9\): Not equivalent.
  6. Response: \(2x - 3x + 2 - 11\): This simplifies to \(-x - 9\) which is exactly the same.
  7. Response: \(-x + 13\): Not equivalent.

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

  1. \(-x - 9\)
  2. \(2x - 3x + 2 - 11\) (which simplifies to \(-x - 9\))

Thus, the correct responses are:

  • \(-x - 9\)
  • \(2x - 3x + 2 - 11\)