Question

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

4(x+3)−10+6x

(2 points)
Responses

4x+12−10+6x


−2x−7


2(5x+1)


10x −7


2(8x+1)


4x+3−10+6x

Answer 1

To find the two expressions that are equivalent to \( 4(x+3)-10+6x \), let's first simplify the given expression step by step.

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

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

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

Now, we see that the original expression simplifies to \( 10x + 2 \).

Next, let's analyze the response options to see which ones are equivalent to \( 10x + 2 \).

1. \( 4x + 12 - 10 + 6x \)
- This simplifies to \( 10x + 2 \), which is equivalent.

2. \( -2x - 7 \)
- This is not equivalent.

3. \( 2(5x + 1) \)
- This simplifies to \( 10x + 2 \), which is equivalent.

4. \( 10x - 7 \)
- This is not equivalent.

5. \( 2(8x + 1) \)
- This simplifies to \( 16x + 2 \), which is not equivalent.

6. \( 4x + 3 - 10 + 6x \)
- This simplifies to \( 10x - 7 \), which is not equivalent.

Thus, the TWO expressions that are equivalent to the original expression are:

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