Select the TWO expressions that are equivalent to the given expression. (2x+2)−(3x+11) (2 points) Responses 5x+13 5 x plus 13 2x−3x+2−11 2 x minus 3 x plus 2 minus 11 2x−3x+2+11 2 x minus 3 x plus 2 plus 11 5x+9 5 x plus 9 −x+13 negative x plus 13 −x−9 negative x minus 9 −x+9

Answer 1

To simplify the expression \((2x+2) - (3x+11)\), we can distribute the negative sign to the second part of the expression:

\[ (2x + 2) - (3x + 11) = 2x + 2 - 3x - 11 \]

Now, combine like terms:

\[ 2x - 3x + 2 - 11 = -x + 2 - 11 = -x - 9 \]

Thus, the simplified expression is \(-x - 9\).

Now, we can check which of the given responses are equivalent to \(-x - 9\):

1. 5x + 13 ≠ \(-x - 9\)
2. 2x - 3x + 2 - 11 = \(-x - 9\) (this simplifies correctly)
3. 2x - 3x + 2 + 11 = \(-x + 13\) (not equivalent)
4. 5x + 9 ≠ \(-x - 9\)
5. -x + 13 ≠ \(-x - 9\)
6. -x - 9 (this is equivalent)
7. -x + 9 ≠ \(-x - 9\)

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

• 2x - 3x + 2 - 11
• -x - 9

So, the correct answers are:

• 2x - 3x + 2 - 11
• -x - 9