Question

Select ALL of the expressions that are equivalent to

4(x+3)−10+6x


(1 point)
Responses

10x−7
10 x minus 7

−2x−7
negative 2 x minus 7

2(5x+1)
2 times open paren 5 x plus 1 close paren

2(8x+1)
2 times open paren 8 x plus 1 close paren

4x+3−10+6x
4 x plus 3 minus 10 plus 6 x

4x+12−10+6x

Answer 1

To determine the expressions that are equivalent to \( 4(x+3)-10+6x \), we should first simplify the given expression step-by-step:

1. Distribute the \( 4 \) inside the parentheses:
\[
4(x+3) = 4x + 12
\]

2. Substitute this back into the expression:
\[
4x + 12 - 10 + 6x
\]

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

4. Putting it together, we have:
\[
10x + 2
\]

Now, we will evaluate each of the provided expressions to find those that are equivalent to \( 10x + 2 \):

1. **\( 10x - 7 \)**: Not equivalent, since \( 10x + 2 \neq 10x - 7 \).

2. **\( -2x - 7 \)**: Not equivalent, as it does not match \( 10x + 2 \).

3. **\( 2(5x + 1) \)**:
\[
2(5x + 1) = 10x + 2
\]
Equivalent.

4. **\( 2(8x + 1) \)**:
\[
2(8x + 1) = 16x + 2
\]
Not equivalent.

5. **\( 4x + 3 - 10 + 6x \)**:
\[
4x + 3 - 10 + 6x = 10x - 7
\]
Not equivalent.

6. **\( 4x + 12 - 10 + 6x \)**:
\[
4x + 12 - 10 + 6x = 10x + 2
\]
Equivalent.

Based on these calculations, the expressions that are equivalent to \( 4(x+3)-10+6x \) are:

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

Thus, the correct responses are:

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