https://r2.erweima.ai/mathbot/image/1726953696268foz39q3p.jpg

The expression in the image appears to be the following:

\[
\left( \frac{3}{2} - 7 \right)^2 \cdot \frac{2}{11} + \left( 1 - \frac{6}{7} \right) = ?
\]

Let me break it down step by step and solve this.

### Step-by-step breakdown:
1. Start by simplifying \(\frac{3}{2} - 7\):
   \[
   \frac{3}{2} - 7 = \frac{3}{2} - \frac{14}{2} = \frac{-11}{2}
   \]

2. Square the result:
   \[
   \left( \frac{-11}{2} \right)^2 = \frac{121}{4}
   \]

3. Multiply by \(\frac{2}{11}\):
   \[
   \frac{121}{4} \cdot \frac{2}{11} = \frac{121 \cdot 2}{4 \cdot 11} = \frac{242}{44} = \frac{121}{22}
   \]

4. Simplify \(1 - \frac{6}{7}\):
   \[
   1 - \frac{6}{7} = \frac{7}{7} - \frac{6}{7} = \frac{1}{7}
   \]

5. Add the two results together:
   \[
   \frac{121}{22} + \frac{1}{7}
   \]

To add these fractions, find a common denominator:
   \[
   \frac{121}{22} = \frac{847}{154}, \quad \frac{1}{7} = \frac{22}{154}
   \]
   \[
   \frac{847}{154} + \frac{22}{154} = \frac{869}{154}
   \]

Thus, the final answer is:

\[
\frac{869}{154}
\]

Would you like more details or clarifications on any step?

Here are some related questions to explore:
1. How do you find a common denominator for adding fractions?
2. What happens when you square a negative fraction?
3. How do you multiply two fractions together?
4. What is the method for simplifying fractions?
5. How can complex expressions involving fractions be broken down efficiently?

**Tip:** Always simplify fractions at the end to avoid unnecessary complexity in calculations!

Learn how to solve the expression (3/2 - 7)^2 * (2/11) + (1 - 6/7) step-by-step. This problem involves algebraic operations, fraction simplifications, exponents, and basic arithmetic suitable for Grades 8-10 students.

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