Let's solve the expression step by step:

Given expression:  
\[
\frac{5 + 8 \times (3 + 2)}{9} - 1
\]

### Step 1: Solve the parentheses first.
\[
3 + 2 = 5
\]

Now, the expression becomes:  
\[
\frac{5 + 8 \times 5}{9} - 1
\]

### Step 2: Multiply.
\[
8 \times 5 = 40
\]

Now, the expression is:  
\[
\frac{5 + 40}{9} - 1
\]

### Step 3: Add.
\[
5 + 40 = 45
\]

Now, the expression becomes:  
\[
\frac{45}{9} - 1
\]

### Step 4: Divide.
\[
\frac{45}{9} = 5
\]

### Step 5: Subtract.
\[
5 - 1 = 4
\]

### Final Answer:
\[
\boxed{4}
\]

Would you like further details or have any other questions?

Here are 5 related questions for further practice:
1. What is the value of \( 6 + 4 \times (2 + 3) - 7 \)?
2. Solve \( [3 + 6 \times (2 + 4)] ÷ 3 - 2 \).
3. What is \( \frac{7 + 2 \times (4 + 5)}{3} - 2 \)?
4. Simplify \( 4 \times (5 + 6) ÷ 2 - 3 \).
5. What is the result of \( 8 ÷ 2 \times (3 + 1) - 5 \)?

**Tip:** Always solve the operations inside parentheses first when working with expressions.

This detailed step-by-step solution solves the expression [5+8x(3+2)]÷9-1 by using the order of operations (PEMDAS). Key steps include solving the parentheses, multiplication, division, and subtraction. Suitable for students in Grades 6-8.

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