To solve the expression \(1288:23 + 81 \cdot 29 - 42 \cdot 28 - 799\), we will follow the order of operations (also known as PEMDAS/BODMAS):
- Division and Multiplication from left to right
- Addition and Subtraction from left to right
Let's break it down step by step.
Division: \(1288:23\) \[ 1288 \div 23 \approx 56 \]
Multiplication: \(81 \cdot 29\) \[ 81 \cdot 29 = 2349 \]
Multiplication: \(42 \cdot 28\) \[ 42 \cdot 28 = 1176 \]
Now the expression is simplified to: \[ 56 + 2349 - 1176 - 799 \]
- Now perform the addition and subtraction from left to right:
First, add \(56 + 2349\): \[ 56 + 2349 = 2405 \]
Next, subtract \(1176\): \[ 2405 - 1176 = 1229 \]
Finally, subtract \(799\): \[ 1229 - 799 = 430 \]
Therefore, the final result of the expression \(1288:23 + 81 \cdot 29 - 42 \cdot 28 - 799\) is \[ \boxed{430} \]