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

(2x+2)−(3x+11)


(1 point)
Responses

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

−x−9
negative x minus 9

5x+13
5 x plus 13

5x+9
5 x plus 9

−x+9
negative x plus 9

−x+13
negative x plus 13

2x−3x+2−11

1 answer

To solve the expression \((2x + 2) - (3x + 11)\), we will first simplify it step by step:

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

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

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

Now let's evaluate the options:

  1. 2x−3x+2+11

    • This simplifies to \((-1x) + 13\) which is not equivalent.

  2. −x−9

    • This is the exact simplified expression we found.

  3. 5x+13

    • This is not equivalent.

  4. 5x+9

    • This is not equivalent.

  5. −x+9

    • This is not equivalent.

  6. −x+13

    • This is not equivalent.

  7. 2x−3x+2−11

    • This simplifies to \((-x) + (2 - 11)\) = \(-x - 9\), which is equivalent.

The two correct responses that are equivalent to the original expression \((2x + 2) - (3x + 11)\) are:

  • −x−9
  • 2x−3x+2−11