To simplify the expression \( 3 \cdot (5 + 2) : 2 \), we will follow the order of operations.
First, calculate the expression inside the parentheses: \[ 5 + 2 = 7 \]
Now, substitute the result back into the expression: \[ 3 \cdot 7 : 2 \]
Next, we can interpret the colon (:) as division, so we rewrite the expression as: \[ \frac{3 \cdot 7}{2} \]
Multiply \( 3 \cdot 7 \): \[ 3 \cdot 7 = 21 \]
Now divide by 2: \[ \frac{21}{2} = 10.5 \]
So, the final result of the expression \( 3 \cdot (5 + 2) : 2 \) is \( 10.5 \).