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.

Solve the inequality and graph the solutions. Check your answer. 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 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 ≥ –(11) 10 ≥ –11

Solve for “y”, then graph the solution. -3 -3 y  -4  -2 -6 -4 6 4 2

Solve for “y”, then graph the solution. -2 -6 -4 6 4 2

Solve for “y”, then graph the solution. -2 -6 -4 6 4 2

Solve for “y”, then graph the solution. -2 -6 -4 6 4 2

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) 16 18 20 22 24 10 14 26 28 30 12

Assignment Pg 182 (2-42) even