Let's solve the inequality \(\frac{3x = 5}{6} > 7\).

1. **Step 1: Simplify the inequality.**
   \[
   \frac{3x = 5}{6} > 7
   \]
   The numerator, \(3x = 5\), suggests an equation rather than an expression. It might be a typo. Assuming you meant \(\frac{3x + 5}{6} > 7\), we can proceed.

2. **Step 2: Multiply both sides by 6.**
   \[
   3x + 5 > 42
   \]

3. **Step 3: Subtract 5 from both sides.**
   \[
   3x > 37
   \]

4. **Step 4: Divide both sides by 3.**
   \[
   x > \frac{37}{3}
   \]
   \[
   x > 12.33\ldots
   \]

The solution is \(x > 12.\overline{3}\).

Let me know if you need more details or have any questions. Here are some related problems:

1. Solve \(\frac{3x - 4}{6} > 5\).
2. Solve \(\frac{2x + 7}{5} \geq 4\).
3. Find the value of \(x\) if \(\frac{4x + 2}{8} = 3\).
4. Solve \(3x + 5 < 20\).
5. Solve \(4x - 3 \leq 15\).

**Tip:** Always double-check the problem's given structure to ensure clarity before solving!

This solution shows how to solve the inequality (3x + 5) / 6 > 7 step-by-step. It covers key algebraic concepts and teaches how to simplify inequalities. Suitable for students in Grades 8-10.

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