Question

Use the order of operations to simplify the following expression: 12−8÷4+[(6+2)−3]2 x 3

Correct Answer: 1 point

Show Work: 1 point

(2 points)

Answer 1

Let's simplify the expression step by step, using the order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

The expression is:
\[ 12 - 8 \div 4 + [(6 + 2) - 3] \cdot 2 \cdot 3 \]

1. **Parentheses/Brackets:**
- Simplify \( (6 + 2) \):
\[ 6 + 2 = 8 \]
- Now the expression looks like:
\[ 12 - 8 \div 4 + [8 - 3] \cdot 2 \cdot 3 \]
- Next, simplify \( [8 - 3] \):
\[ 8 - 3 = 5 \]
- Now it becomes:
\[ 12 - 8 \div 4 + 5 \cdot 2 \cdot 3 \]

2. **Exponents:**
- There are no exponents to simplify.

3. **Multiplication and Division (from left to right):**
- First, tackle \( 8 \div 4 \):
\[ 8 \div 4 = 2 \]
- Now the expression becomes:
\[ 12 - 2 + 5 \cdot 2 \cdot 3 \]
- Next, calculate \( 5 \cdot 2 \):
\[ 5 \cdot 2 = 10 \]
- Multiply \( 10 \cdot 3 \):
\[ 10 \cdot 3 = 30 \]
- Now the expression is:
\[ 12 - 2 + 30 \]

4. **Addition and Subtraction (from left to right):**
- First, perform \( 12 - 2 \):
\[ 12 - 2 = 10 \]
- Then, add \( 10 + 30 \):
\[ 10 + 30 = 40 \]

So, the simplified result of the expression is:
\[ \boxed{40} \]