NAME DATE PERIOD 2.3 Solving Inequalities by Multiplication and Division Solve Inequalities by Multiplication If each side of an inequality is multiplied by the same positive number, the resulting inequality is also true. However, if each side of an inequality is multiplied by the same negative number, the direction of the inequality must be reversed for the resulting inequality to be true. For all numbers a, b, and c, with c # 0, Multiplication 1. if c is positive and a > b, then ac > bc; Property of if c is positive and a b, then ac bc. The property is also true when > and 22 3. 2-3 4. 11. 25.4 12. 2 -6 Define a variable, write an inequality, and solve each problem. Check your solution. 13. Half of a number is at least 14. 14. The opposite of one-third a number is greater than 9. 15. One fifth of a number is at most 30.NAME DATE PERIOD 2-3 Solving Inequalities by Multiplication and Division Solve Inequalities by Division If each side of a true inequality is divided by the same positive number, the resulting inequality is also true. However, if each side of an inequality is divided by the same negative number, the direction of the inequality symbol must be reversed for the resulting inequality to be true. Division For all numbers a, b, and c with c # 0, Property of 1. if c is positive and a > b, then > ; if c is positive and a b, then . The property is also true when > and and s. Example: Solve -12p 2 48. -12y 2 48 Original inequality Divide each side by -12 and change > to S. J'S -4 Simplify. The solution is { yly s-4). Exercises: Solve each inequality. Check your solution. 1. 25g 2-100 2. -2x 29 3. -5c > 2 4. 8m -5p 11. -2n 2 6.2 12. 35 104 14. 1 26 15. -3 Define a variable, write an inequality, and solve each problem. Then check your solution. 17. Four times a number is no more than 108. 18. The opposite of three times a number is greater than 12. 19. Negative five times a number is at most 100