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Let's solve the given problem.

We need to determine which of the listed expressions are equivalent to:

\[
\frac{14x - 21}{7}
\]

To simplify this expression, we divide each term in the numerator by 7:

\[
\frac{14x - 21}{7} = \frac{14x}{7} - \frac{21}{7} = 2x - 3
\]

So, the simplified expression is \( 2x - 3 \).

Now, let's check the options:

1. \( 14x - \frac{21}{7} \): This is not equivalent to \( 2x - 3 \).
2. \( \frac{14x}{7} - \frac{21}{7} \): This simplifies directly to \( 2x - 3 \), so it's equivalent.
3. \( -1x \): This is not equivalent to \( 2x - 3 \).
4. \( 7x - 14 \): This is not equivalent to \( 2x - 3 \).
5. \( \frac{14}{7}x - \frac{21}{7} \): This simplifies to \( 2x - 3 \), so it's equivalent.
6. \( 2x - 3 \): This is exactly the simplified form of the expression, so it's correct.

The correct answers are:

- Option 2: \( \frac{14x}{7} - \frac{21}{7} \)
- Option 5: \( \frac{14}{7}x - \frac{21}{7} \)
- Option 6: \( 2x - 3 \)

Would you like further explanation, or do you have any questions?

### Related Questions:
1. How do you simplify expressions by factoring out common terms?
2. What is the process of simplifying rational expressions?
3. How do you identify equivalent algebraic expressions?
4. Can two different-looking algebraic expressions be equivalent?
5. How does distribution of terms affect the simplification process?

**Tip:** Always check if each term in a polynomial can be divided by the denominator when simplifying a rational expression.

Which of the following are equivalent to this expression? (14x - 21) / 7

Learn how to simplify the algebraic expression (14x - 21) / 7 step by step. This problem involves dividing polynomials by scalars and checking for equivalent expressions. Suitable for students in Grades 6-8.

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