In a medium bowl, whisk together the mayonnaise, vinegar, lemon juice, sugar, salt and pepper until smooth.
In a large bowl combine the cabbage and carrots.
Pour the dressing over the cabbage mixture and stir well to combine. Let the coleslaw sit for 30 minutes before serving, for the cabbage to soften slightly and flavors to combine. Season with more salt and pepper to taste.
Notes
Substitute the apple cider vinegar with distilled white vinegar or white wine vinegar if needed.
To vary the flavor, you can add up to ½ cup of thinly sliced red onion or green onions. You can also add up to ¼ cup of chopped fresh herbs, such as parsley, dill, or cilantro. I also love to add a teaspoon of celery seed to my slaw!