Let's solve the expression step by step:

Given expression:
\[
2x\{11 + [2x(20 - 15 + 8x3)] + 1\}
\]

### Step 1: Simplify inside the parentheses.
Start with the innermost parentheses:
\[
20 - 15 + 8x3
\]
Calculate \(20 - 15\):
\[
20 - 15 = 5
\]
Then multiply:
\[
8x3 = 24
\]
Add these results:
\[
5 + 24 = 29
\]
So the expression inside the parentheses becomes:
\[
2x(29)
\]

### Step 2: Multiply 2 by 29:
\[
2x29 = 58
\]

### Step 3: Replace back into the expression:
\[
2x\{11 + [58] + 1\}
\]

### Step 4: Simplify inside the braces:
\[
11 + 58 + 1 = 70
\]
Now the expression becomes:
\[
2x70
\]

### Step 5: Final multiplication:
\[
2x70 = 140
\]

So, the final result is:
\[
\boxed{140}
\]

Would you like any further details or explanations?

### Related Questions:
1. How do you handle expressions with multiple sets of parentheses?
2. What is the order of operations in mathematical expressions?
3. How can you solve more complex expressions with nested parentheses?
4. How would you handle an expression with division and subtraction included?
5. Can expressions like this be simplified using distributive properties?

### Tip:
Always work from the innermost parentheses outwards when simplifying expressions with multiple layers of parentheses.

Explore how to simplify the expression 2x{11+[2x(20-15+8x3)]+1} using the order of operations (PEMDAS) step by step. This problem is ideal for students in Grades 5-7, covering key algebraic concepts and simplification techniques.

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