Question

Select ALL of the expressions that are equivalent to

4(x+3)−10+6x

(1 point)
Responses

10x−7

−2x−7

2(5x+1)

2(8x+1)

4x+3−10+6x

4x+12−10+6x

Answer 1

To determine the equivalent expressions to \( 4(x+3) - 10 + 6x \), we can simplify it step by step:

1. Distribute \( 4 \) in \( 4(x+3) \):
\[
4(x+3) = 4x + 12
\]

2. Substitute that back into the expression:
\[
4(x+3) - 10 + 6x = (4x + 12) - 10 + 6x
\]

3. Combine like terms:
\[
4x + 12 - 10 + 6x = 4x + 2 + 6x = (4x + 6x) + 2 = 10x + 2
\]

Now we will evaluate each of the provided responses to see if they match \( 10x + 2 \).

1. **Response: \( 10x - 7 \)**
Not equivalent to \( 10x + 2 \).

2. **Response: \( -2x - 7 \)**
Not equivalent to \( 10x + 2 \).

3. **Response: \( 2(5x + 1) \)**
Simplifying it:
\[
2(5x + 1) = 10x + 2 \quad \text{(Equivalent to \( 10x + 2 \))}
\]

4. **Response: \( 2(8x + 1) \)**
Simplifying it:
\[
2(8x + 1) = 16x + 2 \quad \text{(Not equivalent to \( 10x + 2 \))}
\]

5. **Response: \( 4x + 3 - 10 + 6x \)**
Combining like terms:
\[
4x + 3 - 10 + 6x = (4x + 6x) + (3 - 10) = 10x - 7 \quad \text{(Not equivalent to \( 10x + 2 \))}
\]

6. **Response: \( 4x + 12 - 10 + 6x \)**
Combining:
\[
4x + 12 - 10 + 6x = (4x + 6x) + (12 - 10) = 10x + 2 \quad \text{(Equivalent to \( 10x + 2 \))}
\]

Now we can summarize the equivalent expressions:

- **\( 2(5x + 1) \)**
- **\( 4x + 12 - 10 + 6x \)**

Thus, the expressions equivalent to \( 4(x+3) - 10 + 6x \) are:

- \( 2(5x+1) \)
- \( 4x + 12 - 10 + 6x \)

So the final answer is:
- **\( 2(5x + 1) \)**
- **\( 4x + 12 - 10 + 6x \)**