The given expression is:

\[
2x - 7 - x + \frac{7}{2} - 7
\]

Let's simplify this step by step:

1. **Combine like terms involving \( x \):**
   \[
   2x - x = x
   \]

2. **Combine the constant terms \(-7\) and \(-7\):**
   \[
   -7 - 7 = -14
   \]

3. **Now, the expression simplifies to:**
   \[
   x - 14 + \frac{7}{2}
   \]

4. **Combine the constants \(-14\) and \(\frac{7}{2}\):**

   Convert \(-14\) to a fraction with a denominator of 2:
   \[
   -14 = \frac{-28}{2}
   \]

   Add the fractions:
   \[
   \frac{-28}{2} + \frac{7}{2} = \frac{-28 + 7}{2} = \frac{-21}{2}
   \]

So, the simplified expression is:

\[
x - \frac{21}{2}
\]

Would you like any further details or explanations?

---

Here are some related questions:

1. How would you handle the simplification if the expression had additional variables?
2. What happens if you substitute a specific value for \(x\) in the simplified expression?
3. Can you explain the steps to combine like terms in a more complex algebraic expression?
4. How does fraction addition work when denominators are different?
5. How do you simplify expressions with multiple fractions and variables?
6. How would this process change if the original expression was a quadratic equation?
7. What are some common mistakes made when simplifying algebraic expressions?
8. How can you verify the accuracy of your simplification?

**Tip:** Always combine like terms and simplify fractions step by step to avoid errors.

Learn how to simplify the algebraic expression 2x - 7 - x + 7/2 - 7 step by step. This problem covers key algebraic concepts such as combining like terms and fraction arithmetic. Suitable for students in Grades 7-9.

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