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The problem asks you to identify the expression that is **NOT equivalent** to:

\[
\frac{6x + 7}{6}
\]

Let's evaluate each of the options to determine which one is not equivalent.

### Option 1: \(\frac{1}{6} (6x + 7)\)
This expression can be distributed as:

\[
\frac{1}{6} \times (6x + 7) = \frac{1}{6} \times 6x + \frac{1}{6} \times 7 = x + \frac{7}{6}
\]

This is equivalent to the given expression.

### Option 2: \((6x + 7) \div 6\)
Dividing the expression by 6 gives:

\[
\frac{6x + 7}{6}
\]

This is exactly the same as the given expression, so it is equivalent.

### Option 3: \(x + 7\)
This expression is **not** equivalent to \(\frac{6x + 7}{6}\), because it simplifies incorrectly. The original expression divides both \(6x\) and 7 by 6, while this option does not.

### Option 4: \(x + \frac{7}{6}\)
This is exactly what we obtained when simplifying Option 1. Thus, it is equivalent to the given expression.

### Conclusion:
The expression that is **not** equivalent is **Option 3: \(x + 7\)**.

---

Would you like further clarification or details? Here are five questions you could explore:

1. How do you simplify fractions involving polynomials?
2. Can you explain the concept of equivalent expressions in algebra?
3. What is the process for distributing terms in an expression like \(\frac{1}{6}(6x+7)\)?
4. How would this problem change if the numerator was \(6x + 8\) instead?
5. What are other methods to check if two expressions are equivalent?

**Tip:** Always verify equivalence by simplifying each expression step by step.

Identifica la expresión que NO es equivalente a: (6x+7)/6

Learn how to identify expressions that are equivalent to (6x+7)/6 by using distributive properties and algebraic simplification. Suitable for students in Grades 7-9, this problem tests your ability to work with fractions and polynomial expressions.

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