Question

Question

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

(2x+2)−(3x+11)


(2 points)
Responses

−x−9
negative x minus 9

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

5x+9
5 x plus 9

5x+13
5 x plus 13

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

−x+13
negative x plus 13

−x+9

Answer 1

To determine which two expressions are equivalent to the expression \( (2x+2)-(3x+11) \), we first simplify the original expression.

Starting with:

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

Distributing the negative sign:

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

Now, combine like terms:

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

So the simplified form of the expression is \( -x - 9 \).

Now, we will evaluate the provided options to find the equivalent expressions:

1. \(-x - 9\): This is equivalent to the original expression.

2. \(2x - 3x + 2 - 11\): Simplifying this gives: \[ -x + 2 - 11 = -x - 9 \] This is also equivalent.

3. \(5x + 9\): This does not simplify to the original expression.

4. \(5x + 13\): This also does not simplify to the original expression.

5. \(2x - 3x + 2 + 11\): Simplifying gives: \[ -x + 2 + 11 = -x + 13 \] This is not equivalent.

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

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

The two equivalent expressions are:

1. \(-x - 9\)
2. \(2x - 3x + 2 - 11\)

These two expressions are equivalent to the given expression.