This image breaks down the algebraic steps to solve for x in a fractional equation, showing transposition and cross-multiplication clearly.

The problem involves solving the equation:

\[
\frac{3x+1}{x} \times \frac{21}{4} = \frac{35}{2}
\]

Let's go through the solution step by step, ensuring clarity and correctness.

---

Step 1: Simplify the given equation

The equation is:
\[
\frac{3x+1}{x} \times \frac{21}{4} = \frac{35}{2}
\]

First, combine the fractions on the left-hand side:
\[
\frac{(3x+1) \cdot 21}{x \cdot 4} = \frac{35}{2}
\]

This simplifies to:
\[
\frac{21(3x+1)}{4x} = \frac{35}{2}
\]

---

Step 2: Eliminate the fraction by cross-multiplication

To eliminate the fractions, cross-multiply:
\[
2 \cdot 21(3x+1) = 35 \cdot 4x
\]

Simplify both sides:
\[
42(3x+1) = 140x
\]

---

Step 3: Distribute and simplify

Distribute the 42 on the left-hand side:
\[
42 \cdot 3x + 42 \cdot 1 = 140x
\]
\[
126x + 42 = 140x
\]

---

Step 4: Isolate the variable \( x \)

Subtract \( 126x \) from both sides to get all \( x \)-terms on one side:
\[
42 = 140x - 126x
\]
\[
42 = 14x
\]

---

Step 5: Solve for \( x \)

Divide both sides by 14:
\[
x = \frac{42}{14}
\]
\[
x = 3
\]

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Final Answer:

The solution to the equation is:
\[
\boxed{\frac{37}{9}}
\]

However, upon rechecking the steps, it appears there was a discrepancy in the provided solution. The correct solution based on the steps shown should be \( x = 3 \). If the provided solution is \( \frac{37}{9} \), there might be an error in the initial problem setup or transcription. Please verify the original problem statement.

If the problem is as stated in the image, the correct solution is:
\[
\boxed{3}
\]