问题


There is a single choice question about high school mathematics. Answer the question by replying A, B, C or D.
Question: Simplify $\frac{k-3}{2} + 3k+1+\frac{3k+1}{2}$.
A. 3k+1
B. 5k
C. 3k
D. 1
Answer:

答案

模型 模型答案 正确答案
金声玉亮2.0

B. 5k
B
deepseekr1

To simplify the expression \(\frac{k-3}{2} + 3k + 1 + \frac{3k+1}{2}\), follow these steps:

1. **Combine the fractions**:
\[
\frac{k-3}{2} + \frac{3k+1}{2} = \frac{(k-3) + (3k+1)}{2} = \frac{4k - 2}{2} = 2k - 1.
\]

2. **Add the remaining terms**:
Combine \(2k - 1\) with \(3k + 1\):
\[
2k - 1 + 3k + 1 = 5k + 0 = 5k.
\]

**Verification**:
Alternatively, convert all terms to fractions with denominator 2:
\[
\frac{k-3}{2} + \frac{6k}{2} + \frac{2}{2} + \frac{3k+1}{2} = \frac{(k-3) + 6k + 2 + 3k + 1}{2} = \frac{10k}{2} = 5k.
\]

Thus, the simplified expression is **\(5k\)**, corresponding to **Option B**.

**Answer: B**
B
gpto1 B B
GPT-4o To simplify the expression \(\frac{k-3}{2} + 3k + 1 + \frac{3k+1}{2}\), we first combine the terms with a common denominator and then simplify the result.

1. Combine the fractional terms:
\[
\frac{k-3}{2} + \frac{3k+1}{2} = \frac{(k-3) + (3k+1)}{2} = \frac{k - 3 + 3k + 1}{2} = \frac{4k - 2}{2} = 2k - 1
\]

2. Add the remaining terms:
\[
2k - 1 + 3k + 1 = 2k + 3k - 1 + 1 = 5k
\]

Therefore, the simplified expression is \(5k\).

Answer: B
B
llama3.1-70B-Instruct

B
B
llama3.1-405B-Instruct

To simplify the expression, we can start by combining the like terms:

$$\frac{k-3}{2} + 3k+1+\frac{3k+1}{2}$$

First, let's combine the fractions:

$$\frac{k-3}{2} + \frac{3k+1}{2} = \frac{k-3+3k+1}{2} = \frac{4k-2}{2} = 2k-1$$

Now, let's add the remaining terms:

$$2k-1 + 3k+1 = 5k$$

So, the simplified expression is:

$$5k$$

The correct answer is:

B. 5k
B
DeepSeek-Coder-V2 B. 5k B
Qwen2-72B-Instruct B. 5k

Explanation: To simplify the expression, combine like terms and simplify the fractions.
$\frac{k-3}{2} + 3k+1+\frac{3k+1}{2} = \frac{k-3+6k+2+3k+1}{2} = \frac{10k}{2} = 5k$
B
baichuan4 To simplify the expression, we first need to combine the fractions with a common denominator. The denominator in this case is 2. We can rewrite the expression as follows:

$\frac{k-3}{2} + 3k + 1 + \frac{3k+1}{2}$

Now, let's combine the fractions:

$\frac{(k-3) + 2(3k+1)}{2} + 3k + 1$

$\frac{k-3+6k+2}{2} + 3k + 1$

$\frac{7k-1}{2} + 3k + 1$

Now, let's convert the whole number terms into fractions with a denominator of 2:

$\frac{7k-1}{2} + \frac{6k+2}{2}$

Now, we can add the fractions:

$\frac{7k-1+6k+2}{2}$

$\frac{13k+1}{2}$

The correct answer is not listed among the options provided. The simplified expression is $\frac{13k+1}{2}$.
B
doubao First, find a common denominator for the fractions:

\[
\begin{align*}
&\frac{k-3}{2}+3k+1+\frac{3k+1}{2}\\
=&\frac{k-3}{2}+\frac{6k}{2}+\frac{2}{2}+\frac{3k+1}{2}\\
=&\frac{k-3+6k+2+3k+1}{2}\\
=&\frac{(k+6k+3k)+(-3+2+1)}{2}\\
=&\frac{10k}{2}\\
=&5k
\end{align*}
\]

So the answer is B.
B
minimax To simplify the expression $\frac{k-3}{2} + 3k+1+\frac{3k+1}{2}$, we combine like terms and simplify the fractions:

First, let's combine the fractions:

$\frac{k-3}{2} + \frac{3k+1}{2} = \frac{(k-3) + (3k+1)}{2}$

Now, simplify the numerator:

$(k-3) + (3k+1) = k + 3k - 3 + 1 = 4k - 2$

So the combined fraction is:

$\frac{4k - 2}{2}$

Now, we can simplify this fraction by dividing both the numerator and the denominator by 2:

$\frac{4k - 2}{2} = \frac{2(2k - 1)}{2} = 2k - 1$

Now, let's add this to the remaining terms in the original expression:

$2k - 1 + 3k + 1$

Combine like terms:

$(2k + 3k) + (-1 + 1) = 5k + 0 = 5k$

So the simplified expression is:

$5k$

The correct answer is:

B. 5k
B
kimi First, let's simplify the given expression step by step:

$\frac{k-3}{2} + 3k+1+\frac{3k+1}{2}$

Combine the fractions:

$= \frac{k-3}{2} + \frac{3k+1}{2} + 3k+1$

Since the fractions have the same denominator, you can add the numerators:

$= \frac{k-3+3k+1}{2} + 3k+1$

Simplify the numerator:

$= \frac{4k-2}{2} + 3k+1$

Divide the numerator by the denominator:

$= 2k-1 + 3k+1$

Combine like terms:

$= 5k$

So the simplified expression is $5k$.

Answer: B. 5k
B
wenxinyiyan B

Explanation:
Given expression:
$\frac{k-3}{2} + 3k+1+\frac{3k+1}{2}$

To simplify, first find a common denominator, which in this case is 2. Then, bring all terms to that common denominator:
$= \frac{k - 3}{2} + \frac{2(3k + 1)}{2} + \frac{3k + 1}{2}$

Combine all terms into a single fraction:
$= \frac{k - 3 + 6k + 2 + 3k + 1}{2}$

Simplify the numerator:
$= \frac{10k}{2}$
$= 5k$

So, the simplified expression is $5k$.
B
zhipu To simplify the expression \(\frac{k-3}{2} + 3k + 1 + \frac{3k+1}{2}\), we can follow these steps:

1. Combine the fractions with a common denominator:
\[
\frac{k-3}{2} + \frac{3k+1}{2}
\]

2. Add the numerators of the fractions:
\[
\frac{(k-3) + (3k+1)}{2} = \frac{k - 3 + 3k + 1}{2} = \frac{4k - 2}{2}
\]

3. Simplify the fraction:
\[
\frac{4k - 2}{2} = 2k - 1
\]

4. Now add the remaining terms in the original expression:
\[
2k - 1 + 3k + 1
\]

5. Combine like terms:
\[
2k + 3k - 1 + 1 = 5k
\]

So the simplified form of the expression is \(5k\).

The correct answer is B.

Answer: B
B
gpto1 B B
deepseekv3 To simplify the expression \(\frac{k-3}{2} + 3k + 1 + \frac{3k+1}{2}\), follow these steps:

1. **Combine the fractions:**
\[
\frac{k-3}{2} + \frac{3k+1}{2} = \frac{(k-3) + (3k+1)}{2} = \frac{4k - 2}{2} = 2k - 1
\]

2. **Add the remaining terms:**
\[
2k - 1 + 3k + 1 = 5k
\]

Thus, the simplified expression is \(5k\).

**Answer:** \(\boxed{B}\)
B