Okay, we are tasked with adding 1429 and 3759. Let's begin!

Step 1: We'll start by adding the digits 9 & 9 in column 1 and get 18.
We'll write down the last digit 8 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 2 & 5 in column 2 and get 8.

Step 3: We'll start by adding the digits 4 & 7 in column 3 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 1 & 3 in column 4 and get 5.

So, 1429 + 3759 = 5188.

