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

Remember that to simplify this expression, distribute a -1 to each term inside the second parentheses. Then combine like terms.

(2x+2)−(3x+11)

(2 points)
Responses

5x+13
5 x plus 13

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

5x+9
5 x plus 9

−x+9
negative x plus 9

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

−x−9
negative x minus 9

−x+13
negative x plus 13
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1 answer

To simplify the expression \((2x + 2) - (3x + 11)\), we first distribute the \(-1\) to each term in the second parentheses:

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

Now, we combine like terms:

  1. Combine the \(x\) terms: \(2x - 3x = -x\)
  2. Combine the constant terms: \(2 - 11 = -9\)

Putting it all together, we have:

\[ -x - 9 \]

Now, we can select the two expressions that are equivalent to \(-x - 9\):

  1. \(-x - 9\)
  2. The expression \(2x - 3x + 2 - 11\) simplifies to \(-x - 9\) as shown below:
    • \(2x - 3x = -x\)
    • \(2 - 11 = -9\)
    • So, \(2x - 3x + 2 - 11 = -x - 9\)

Therefore, the two equivalent expressions are:

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