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The given expression is:

\[
22 - \left[ 6 - (10 - 4 + 3) \right] \div 2 \times 3
\]

Let’s solve this step-by-step following the order of operations (PEMDAS/BODMAS):

1. **Parentheses** (Innermost first):  
   Start by solving inside the parentheses:
   \[
   (10 - 4 + 3) = 9
   \]
   Now the expression becomes:
   \[
   22 - \left[ 6 - 9 \right] \div 2 \times 3
   \]

2. **Brackets**:  
   Simplify the brackets:
   \[
   6 - 9 = -3
   \]
   Now the expression becomes:
   \[
   22 - (-3) \div 2 \times 3
   \]

3. **Division and Multiplication (left to right)**:
   First, handle the division:
   \[
   (-3) \div 2 = -1.5
   \]
   Now multiply by 3:
   \[
   -1.5 \times 3 = -4.5
   \]
   Now the expression becomes:
   \[
   22 - (-4.5)
   \]

4. **Final subtraction**:
   Subtracting a negative is the same as adding:
   \[
   22 + 4.5 = 26.5
   \]

Thus, the value of the expression is **26.5**.

Would you like more details on any step, or have further questions?

Here are 5 related questions for practice:

1. Solve: \( 15 - [8 - (12 - 3)] \div 3 \times 4 \)
2. Evaluate: \( 30 - [5 - (20 - 10 + 5)] \times 2 \)
3. What is the result of: \( 50 - [7 - (14 - 6)] \div 4 \times 5 \)
4. Simplify: \( 18 - [4 - (9 - 2)] \div 2 \times 3 \)
5. Calculate: \( 25 - [10 - (15 - 8 + 2)] \div 5 \times 4 \)

**Tip:** Always remember the order of operations (PEMDAS/BODMAS) when solving complex expressions. Start with parentheses and work your way out!

Learn how to solve the mathematical expression 22 - [6 - (10 - 4 + 3)] ÷ 2 × 3 step-by-step using the order of operations (PEMDAS/BODMAS). Suitable for students in Grades 5-7.

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