It's not that multiplying both sides by r is wrong- you just have to be careful. If you multiply both sides of an inequality by anegativenumber, youreversethe direction of the inequality.

Yes, as you say, r cannot be 0- so it is either positive or negative. If it is positive, multiplying both sides by r gives which is the same as . If r is negative, multiplying both sides by r gives which is the same as . Obviously, determining where is important in solving those! Don't forget that the first is only true for r> 0 and the second for r< 0.