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

Question

(2x+2)−(3x+11)


(1 point)
Responses

−x+13
negative x plus 13

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

5x+9
5 x plus 9

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

−x+9

Answer 1

To determine which expressions are equivalent to \((2x + 2) - (3x + 11)\), let's simplify the given expression step by step:

1. Start with the original expression: \[ (2x + 2) - (3x + 11) \]

2. Distribute the negative sign across the second parentheses: \[ 2x + 2 - 3x - 11 \]

3. Combine like terms:

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

Putting it all together, we have: \[ -x - 9 \]

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

1. −x + 13: not equivalent
2. 2x − 3x + 2 − 11: simplifies to \(-x - 9\), so this is equivalent.
3. 5x + 9: not equivalent
4. 2x − 3x + 2 + 11: simplifies to \(-x + 13\), so this is not equivalent.
5. −x − 9: this is equivalent.
6. 5x + 13: not equivalent
7. −x + 9: not equivalent

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

1. 2x − 3x + 2 − 11
2. −x − 9