To simplify the expression \((2x + 2) - (3x + 11)\), we can follow these steps:
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Distribute the negative sign: \[ (2x + 2) - (3x + 11) = 2x + 2 - 3x - 11 \]
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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 \(-x - 9\):
- Response: \(-x - 9\): This is exactly the same, so it is equivalent.
- Response: \(-x + 9\): Not equivalent, as the signs are different.
- Response: \(5x + 13\): Not equivalent.
- Response: \(2x - 3x + 2 + 11\): This simplifies to \(-x + 13\), not equivalent.
- Response: \(5x + 9\): Not equivalent.
- Response: \(2x - 3x + 2 - 11\): This simplifies to \(-x - 9\) which is exactly the same.
- Response: \(-x + 13\): Not equivalent.
The TWO expressions that are equivalent to the given expression \((2x + 2) - (3x + 11)\) are:
- \(-x - 9\)
- \(2x - 3x + 2 - 11\) (which simplifies to \(-x - 9\))
Thus, the correct responses are:
- \(-x - 9\)
- \(2x - 3x + 2 - 11\)