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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 ,
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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.
–8 –2 –10 –6 –4 0 2 4 6 8 10 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
Check Check a number greater than 10. Check the endpoint, –10. 10 = –x 10 ≥ –x 10 –(–10) 10 ≥ –(11) 10 10 10 ≥ –11 Check It Out! Solve the inequality and graph the solutions. Check your answer. 10 ≥ –x
6 -6 -4 -2 0 2 4 Solve for “y”, then graph the solution. -3y 12 -3 -3 y -4
6 -6 -4 -2 0 2 4 Solve for “y”, then graph the solution. -4y 16 y -4
6 -6 -4 -2 0 2 4 Solve for “y”, then graph the solution. 3y -15 y -5
6 -6 -4 -2 0 2 4 Solve for “y”, then graph the solution. -5y -20 y 4
Since x is divided by –3, multiply both sides by –3. Change to . 10 14 16 18 20 22 24 26 28 30 12 Solve the inequality and graph the solutions. 24 x (or x 24)