Question

5a) \\(5x - 3 = 3x + 7\\)
\\(= 5x - 3x = 3 + 7\\)
\\(= 2x = 10\\)
\\(= x = 5\\)

5b) \\(4x + 2 = 6x - 8\\)
\\(= 4x - 6x = -2 - 8\\)
\\(= -2x = -10\\)
\\(= x = 5\\)

5c) \\(3x - 5 = 9 - x\\)
\\(= 3x + x = 5 + 9\\)
\\(= 4x = 14\\)
\\(= \frac{7}{2}\\)

Explanation:

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<reasoning>

Solve question 5a

\[

$$\begin{aligned} 5x - 3 &= 3x + 7 \\ 5x - 3x &= 7 + 3 \\ 2x &= 10 \\ x &= 5 \end{aligned}$$

\]

Solve question 5b

\[

$$\begin{aligned} 4x + 2 &= 6x - 8 \\ 4x - 6x &= -8 - 2 \\ -2x &= -10 \\ x &= 5 \end{aligned}$$

\]

Solve question 5c

\[

$$\begin{aligned} 3x - 5 &= 9 - x \\ 3x + x &= 9 + 5 \\ 4x &= 14 \\ x &= \frac{14}{4} = \frac{7}{2} \end{aligned}$$

\]
</reasoning>

<answer>

Question 5a

\(x = 5\)

Question 5b

\(x = 5\)

Question 5c

\(x = \frac{7}{2}\)
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multi-part",
"knowledge_point": [
"Mathematics",
"Algebra",
"Linear Equations"
]
}
</post_analysis>

Answer:

<pre_analysis>
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"step_cot",
"explain_then_answer",
"quick"
],
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"Linear Equations",
"Algebraic Simplification"
],
"new_concepts": [],
"current_concepts": [
"Linear Equations",
"Algebraic Simplification"
]
}
</pre_analysis>

<reasoning>

Solve question 5a

\[

$$\begin{aligned} 5x - 3 &= 3x + 7 \\ 5x - 3x &= 7 + 3 \\ 2x &= 10 \\ x &= 5 \end{aligned}$$

\]

Solve question 5b

\[

$$\begin{aligned} 4x + 2 &= 6x - 8 \\ 4x - 6x &= -8 - 2 \\ -2x &= -10 \\ x &= 5 \end{aligned}$$

\]

Solve question 5c

\[

$$\begin{aligned} 3x - 5 &= 9 - x \\ 3x + x &= 9 + 5 \\ 4x &= 14 \\ x &= \frac{14}{4} = \frac{7}{2} \end{aligned}$$

\]
</reasoning>

<answer>

Question 5a

\(x = 5\)

Question 5b

\(x = 5\)

Question 5c

\(x = \frac{7}{2}\)
</answer>

<post_analysis>
{
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"question_type": "Multi-part",
"knowledge_point": [
"Mathematics",
"Algebra",
"Linear Equations"
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