Question

Select the TWO expressions that are equivalent to the given expression. (2x+2)−(3x+11) (1 point) Responses −x+13 negative x plus 13 5x+9 5 x plus 9 5x+13 5 x plus 13 −x−9 negative x minus 9 2x−3x+2−11 2 x minus 3 x plus 2 minus 11 −x+9 negative x plus 9 2x−3x+2+11

Answer 1

To simplify the expression \((2x + 2) - (3x + 11)\), we follow these steps:

1. Distribute the negative sign across the second parentheses:

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

2. Combine like terms:

- Combine \(2x\) and \(-3x\):
\[
2x - 3x = -x
\]

- Combine \(2\) and \(-11\):
\[
2 - 11 = -9
\]

Thus, the simplified expression is:

\[
-x - 9
\]

Now, let's identify which of the responses given are equivalent to \(-x - 9\):

1. \(-x + 13\) - NOT equivalent
2. \(5x + 9\) - NOT equivalent
3. \(5x + 13\) - NOT equivalent
4. \(-x - 9\) - EQUIVALENT
5. \(2x - 3x + 2 - 11\) - This simplifies to \(-x - 9\) as shown above, so it is EQUIVALENT.
6. \(-x + 9\) - NOT equivalent
7. \(2x - 3x + 2 + 11\) - This simplifies to \(-x + 13\), which is NOT equivalent.

Therefore, the two equivalent expressions are:

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

So the answers are:

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