Question

what is the rule when multiplying or dividing by a negative number to solve inequalities?

Answer 1

You flip the inequality.
Example: if x > -y and you divide both sides by (-1) then you flip the inequality so: -x < y

Answer 2

When we multiply or divide by a negative to solve an inequality, it's the same as multiplying or dividing by a negative to solve a regular equation! Just remember to multiply or divide both sides by the same quantity, then simplify! Remember, when multiplying or dividing by a negative YOU MUST FLIP THE INEQUALITY SIGN.