There's a reasonably large body of evidence that a (small) increase in the minimum wage to e.g. 40% of median local income doesn't have many negative employment effects (or if it does, they are very small). That being said, minimum wage is not a particularly good way to decrease inequality since it's not very well targeted and the negative effects it does have (higher prices, less employer training, etc) seem to mostly hurt the poor. A much better policy would be increasing the EITC.