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4.3 The Multiplication Property of Inequality • Goal: To solve inequalities using the multiplication property Multiplication Property of Inequalities For all rational numbers a, b, and c: When c is positive, if a > b, then a • c > b • c When c is negative, if a > b, then a • c < b • c If you multiply or divide an inequality by a negative number, reverse the inequality sign in the answer. Caution! Do not change the direction of the inequality symbol just because you see a negative sign. For example, you do not change the symbol when solving 4x < –24. Check It Out! Solve the inequality and graph the solutions. Check your answer. 10 ≥ –x divide both sides by –1 to make x positive. Change to . –1(10) ≤ –1(–x) –10 ≤ x –10 –8 –6 –4 –2 0 2 4 6 8 10 Check It Out! Solve the inequality and graph the solutions. Check your answer. 10 ≥ –x Check Check the endpoint, –10. 10 = –x 10 10 –(–10) 10 Check a number greater than 10. 10 ≥ –x 10 10 ≥ –(11) ≥ –11 Solve for “y”, then graph the solution. -3y 12 -3 -3 y -4 -6 -4 -2 0 2 4 6 Solve for “y”, then graph the solution. -4y 16 y -4 -6 -4 -2 0 2 4 6 Solve for “y”, then graph the solution. 3y -15 y -5 -6 -4 -2 0 2 4 6 Solve for “y”, then graph the solution. -5y -20 y4 -6 -4 -2 0 2 4 6 Solve the inequality and graph the solutions. Since x is divided by –3, multiply both sides by –3. Change to . 24 x (or x 24) 10 12 14 16 18 20 22 24 26 28 30 Assignment Pg 182 (2-42) even