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

Question

(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:

• \(-x - 9\)
• \(2x - 3x + 2 - 11\)