Let's break this expression down step by step:

Given expression: 
\[ 2 + [-2 - 5 \{ 7 + 2(3 + 14) \}] \]

### Step 1: Simplify the parentheses first.

Inside the innermost parentheses:
\[ 3 + 14 = 17 \]

Now, substitute this back into the expression:
\[ 2 + [-2 - 5 \{ 7 + 2(17) \}] \]

### Step 2: Simplify the multiplication within the brackets.

Multiply \( 2 \times 17 = 34 \), then substitute:
\[ 2 + [-2 - 5 \{ 7 + 34 \}] \]

### Step 3: Add inside the curly brackets.

\[ 7 + 34 = 41 \]

So, the expression becomes:
\[ 2 + [-2 - 5(41)] \]

### Step 4: Simplify the multiplication.

Multiply \( 5 \times 41 = 205 \), so we get:
\[ 2 + [-2 - 205] \]

### Step 5: Simplify the terms inside the square brackets.

\[ -2 - 205 = -207 \]

Thus, the expression is now:
\[ 2 + (-207) \]

### Step 6: Add the final terms.

\[ 2 + (-207) = -205 \]

### Final Answer:
\[ \boxed{-205} \]

Would you like more details on any of the steps, or do you have any questions?

Here are 5 related questions for further practice:
1. Simplify \( 3 + [-4 - 3\{2 + 5(1 + 2)\}] \).
2. Solve \( 4 + [1 - 6\{8 + 3(2 + 5)\}] \).
3. Evaluate \( 2 + [-3 - 4\{6 + 2(7 + 1)\}] \).
4. Calculate \( 5 + [-1 - 3\{9 + 4(2 + 6)\}] \).
5. Simplify \( 1 + [-3 - 2\{10 + 2(5 + 4)\}] \).

**Tip:** Always start simplifying from the innermost parentheses or brackets.

This problem demonstrates how to simplify the expression 2 + [-2 - 5{7 + 2(3 + 14)}] step-by-step using the order of operations. Follow along to practice using parentheses, brackets, and braces effectively. This solution is ideal for students in Grades 6-8.

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