1. ALGEBRA 1 Lesson 3-3 Warm-Up

2. ALGEBRA 1 Lesson 3-3 Warm-Up

3. ALGEBRA 1 “Solving Inequalities Using Multiplication and Division” (3-3) (3-1) What is the “Multiplication Property of Inequality”? Rule: Multiplication Property of Inequality: If you multiply both sides of an inequality by the same number, the inequality is equivalent to the original inequality. if a > b, then ac > bc if a < b, then ac < b c Example: 3 > 1, so 3(2) > 1(2) Example: 4 < 5, so 4 (2) < 5(2) 6 > 2 8 < 10 Note: This property is also true for ≥ and ≤ Rule: Multiplication Property of Inequality when c < 0: If you multiply both sides of an inequality by a negative number, the inequality sign must be reversed (switched around). if a > b, then a(-c) b(-c) Example: 3 > 1, but 3(-2) 5(-2) -6 -10 Note: This property is also true for ≥ and ≤.

4. ALGEBRA 1 Solve > –2. Graph and check the solution. z3z3 z > –6 Simplify each side. – = –2Substitute –6 for z. 6363 –2 = –2Simplify. – > –2Substitute –3 for z. 3333 –1 > –2Simplify. 3 > 3(–2)Multiply each side by 3. Do not reverse the inequality symbol. z3z3 ( ) Check: = –2 Check the computation. z3z3 z3z3 > –2Check the direction of the inequality. Solving Inequalities Using Multiplication and Division LESSON 3-3 Additional Examples

5. ALGEBRA 1 Solve 3 – x. Graph and check the solution. < –5 x, or x –5Simplify. <> 3535 ( ) 5353 – 5353 – (3) > ( ) 3535 x Multiply each side by the reciprocal of –, which is –, and reverse the inequality symbol. 3535 5353 – Solving Inequalities Using Multiplication and Division LESSON 3-3 Additional Examples

6. ALGEBRA 1 (continued) Check: 3 = – xCheck the computation. 3535 3 = – (–5) Substitute –5 for x. 3535 3 = 3 3 ≤ – x Check the direction of the inequality. 3535 3 ≤ – (–10) Substitute –10 for x. 3535 3 ≤ 6 Simplify. Solving Inequalities Using Multiplication and Division LESSON 3-3 Additional Examples

7. ALGEBRA 1 “Solving Inequalities Using Multiplication and Division” (3-3) (3-1) What is the “Division Property of Inequality”? Rule: Division Property of Inequality: If you divide both sides of an inequality by the same number, the inequality is equivalent to the original inequality. if a > b, then a  c > b  c if a < b, then a  c < b  c Example: 4 > 2, so 4  2 > 2  2 Example: 6 < 10, so 6  2 < 10  2 2 > 1 3 < 5 Note: This property is also true for ≥ and ≤ Rule: Division Property of Inequality when c < 0: If you divide both sides of an inequality by a negative number, the inequality sign must be reversed (switched around). if a > b, then a  -c b  -c Example: 4 > 2, but 4  -2 10  -2 -2 -5 Note: This property is also true for ≥ and ≤.

8. ALGEBRA 1 Solve –4c < 24. Graph the solution. c > –6Simplify. Divide each side by –4. Reverse the inequality symbol. –4c –4 > 24 –4 Solving Inequalities Using Multiplication and Division LESSON 3-3 Additional Examples

9. ALGEBRA 1 Your family budgets $160 to spend on fuel for a trip. How many times can they fill the car’s gas tank if it cost $25 each time? Your family can fill the car’s tank at most 6 times. cost per total fuel tankbudget Words:times number of tanks is at most Define:Let = the number of tanks of gas. t Equation: 25 160t < 25t 160 < t 6.4Simplify. < Divide each side by 25. < 25t 25 160 25 Solving Inequalities Using Multiplication and Division LESSON 3-3 Additional Examples

10. ALGEBRA 1 Solve each inequality. Graph the solution. 1. –3 2.– < –1 3.6x < 30 4.48 –12h y2y2 > p3p3 > y –6 > p > 3 x < 5 > < –4 h, or h –4 Solving Inequalities Using Multiplication and Division LESSON 3-3 Lesson Quiz