Question

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

Answer 1

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