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

(2x+2)−(3x+11)

(1 point)
Responses

2x−3x+2−11

5x+9

−x−9

−x+9

2x−3x+2+11

5x+13

−x+13

1 answer

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

  1. Distribute the minus sign across the second parenthesis: \[ (2x + 2) - (3x + 11) = 2x + 2 - 3x - 11 \]

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

Now we need to identify which of the given responses is equivalent to \(-x - 9\).

Let's check each response:

  1. \(2x - 3x + 2 - 11\): \[ 2x - 3x + 2 - 11 = -x + 2 - 11 = -x - 9 \quad \text{(equivalent)} \]

  2. \(5x + 9\): \[ \text{Not equivalent} \]

  3. \(-x - 9\): \[ \text{Clearly equivalent} \]

  4. \(-x + 9\): \[ \text{Not equivalent} \]

  5. \(2x - 3x + 2 + 11\): \[ 2x - 3x + 2 + 11 = -x + 2 + 11 = -x + 13 \quad \text{(not equivalent)} \]

  6. \(5x + 13\): \[ \text{Not equivalent} \]

  7. \(-x + 13\): \[ \text{Not equivalent} \]

Thus, the two correct equivalent expressions to \((2x+2)−(3x+11)\) are:

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

The two expressions that are equivalent to the given expression are:

  • \(2x - 3x + 2 - 11\)
  • \(-x - 9\)