I have an old Mac and I can't update it to use apps that require newer macOS

MacBookAir4,2 is MacBook Air 13" Mid 2011, and that tops out at macOS 10.13, which is what you're running. So no upgrade options there.

What are you doing with those PDFs? There's a viewer and basic editor built into macOS for common PDF formats, though Adobe adds a bunch of other stuff that only they really support.

What is the MacBook Air model year shown in  > About This Mac? With that, we can tell you your upgrade options.

What are you doing with PDF documents? PDF documents are not normally edited. That format is usually intended for printing or viewing, and not usually for modifications. Which means there might be alternative tools and formats.