Question

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

(2x+2)−(3x+11)


(2 points)
Responses

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

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

5x+13
5 x plus 13

−x+9

Answer 1

To simplify the expression \((2x+2)−(3x+11)\):

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

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

So, the expression simplifies to \(-x - 9\).

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

1. **\(2x - 3x + 2 + 11\)**: This simplifies to \(-x + 13\). **Not equivalent.**

2. **\(5x + 9\)**: This is clearly not equivalent.

3. **\(-x + 13\)**: This is not equivalent to \(-x - 9\).

4. **\(-x - 9\)**: This is exactly the expression we simplified to. **Equivalent.**

5. **\(2x - 3x + 2 - 11\)**: This simplifies to \(-x - 9\). **Equivalent.**

6. **\(5x + 13\)**: This is also not equivalent.

7. **\(-x + 9\)**: This is not equivalent.

Thus, the two expressions that are equivalent to \((2x + 2) - (3x + 11)\) are:
- \(-x - 9\)
- \(2x - 3x + 2 - 11\)