When multiplying and dividing by a negative number one must change the inequality sign so it is reversed. The reasoning being is if one does not change the symbol than you get a false inequality. Negative numbers mirror positive numbers and when so the large numbers are to the left to the smaller numbers. That is why it is important to flip the symbol to receive a true inequality. This happens for equations but it is modified; one cannot change an equation sign but in order to cancel out a negative to solve for a variable one must add, multiply, subtract, or divide by a positive.