Question

Which expressions are equivalent to
\[x+x+x + 2\] ?
Choose 2 answers:
Choose 2 answers:
(Choice A)
\[3x + 2\]
A
\[3x + 2\]
(Choice B)
\[3 + 2x\]
B
\[3 + 2x\]
(Choice C)
\[3(x+2)\]
C
\[3(x+2)\]
(Choice D)
\[2(x+1)+x\]
D
\[2(x+1)+x\]
(Choice E)
\[5x\]
E
\[5x\]

Answer 1

To simplify the expression \(x + x + x + 2\), we can combine the \(x\) terms.

There are three \(x\) terms, so:

\[
x + x + x = 3x
\]

Adding the constant \(2\), we have:

\[
3x + 2
\]

Now, we'll check each of the answer choices to see if they are equivalent to \(3x + 2\):

**Choice A: \(3x + 2\)**
This is equal to the original expression.

**Choice B: \(3 + 2x\)**
This is not equivalent to \(3x + 2\).

**Choice C: \(3(x + 2)\)**
Distributing gives \(3x + 6\), which is not equal to \(3x + 2\).

**Choice D: \(2(x + 1) + x\)**
Distributing \(2\) gives \(2x + 2 + x = 3x + 2\), which matches our expression.

**Choice E: \(5x\)**
This is not equivalent to \(3x + 2\).

The equivalent expressions are:

- **Choice A: \(3x + 2\)**
- **Choice D: \(2(x + 1) + x\)**

So the two correct answers are **Choice A** and **Choice D**.