Question

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

(2x+2)−(3x+11)


(2 points)
Responses

5x+9
5 x plus 9

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

−x+9
negative x plus 9

−x+13
negative x plus 13

−x−9
negative x minus 9

5x+13

Answer 1

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

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 have simplified the expression to \(-x - 9\).

Next, we will check which of the provided responses are equivalent to \(-x - 9\):

1. **5x + 9**: Not equivalent.
2. **2x − 3x + 2 − 11**: This simplifies to \(-x - 9\) (equivalent).
3. **2x − 3x + 2 + 11**: This simplifies to \(-x + 13\) (not equivalent).
4. **−x + 9**: Not equivalent.
5. **−x + 13**: Not equivalent.
6. **−x − 9**: Equivalent (matches our simplified expression).
7. **5x + 13**: Not equivalent.

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

- \(2x − 3x + 2 − 11\)
- \(-x - 9\)

So, the correct responses are:
- \(2x - 3x + 2 - 11\)
- \(-x - 9\)