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 <u>YOU MUST FLIP THE INEQUALITY SIGN.</u>
If you begin with an inequality and wish to solve for one of the variables, you must isolate that variable on the right side of a new inequality. Now supposing that that variable is negative in the given inequality, and that you must change that sign to positive. Generally you can either multiply every term in the given inequality by -1 or divide every term by -1. In both cases you must change the direction of the inequality sign.
Example: Given -3x > 2 + 5y, solve for x. To do this, multiply all three terms in the inequality by (-1/3), which yields x on the left and -2/3 - (5/3)y on the right. <em>We must reverse the direction of the inequality sign</em>, so the final answer is x < -2/3 - (5/3)y.
