### Instruction: What is the smallest positive value of $x$ such that $x + 5678$ results in a palindrome?### Response: A palindrome is a number that reads the same forwards and backwards, like 121 or 686.
To find the smallest value of $x$, I want to make $x + 5678$ as small as possible, but still a palindrome.
The smallest palindrome that is larger than 5678 is 5775, since I can just change the middle digits to match the outer digits.
To get 5775, I need to add 97 to 5678.
So, the smallest value of $x$ is 97.