Lesson Objective: I will be able to … Solve inequalities that contain more than one operation Language Objective: I will be able to … Read, write, and listen about vocabulary, key concepts, and examples

Example 1: Solving Multi-Step Inequalities Page 23 Solve the inequality and graph the solutions. 8 – 3y ≥ 29 Since 8 is added to –3y, subtract 8 from both sides to undo the addition. 8 – 3y ≥ 29 –8 –8 –3y ≥ 21 Since y is multiplied by –3, divide both sides by –3 to undo the multiplication. Change ≥ to ≤. y ≤ –7 –7 –10 –8 –6 –4 –2 2 4 6 8 10

Solve the inequality and graph the solutions. Your Turn 1 Page 24 Solve the inequality and graph the solutions. –12 ≥ 3x + 6 Since 6 is added to 3x, subtract 6 from both sides to undo the addition. –12 ≥ 3x + 6 – 6 – 6 –18 ≥ 3x Since x is multiplied by 3, divide both sides by 3 to undo the multiplication. –6 ≥ x or x ≤ -6 –10 –8 –6 –4 –2 2 4 6 8 10

Example 2: Simplifying Before Solving Inequalities Page 24 Solve the inequality and graph the solutions. –4(2 – x) ≤ 8 −4(2 – x) ≤ 8 Distribute –4 on the left side. −4(2) − 4(−x) ≤ 8 Since –8 is added to 4x, add 8 to both sides. –8 + 4x ≤ 8 +8 +8 4x ≤ 16 Since x is multiplied by 4, divide both sides by 4 to undo the multiplication. x ≤ 4 –10 –8 –6 –4 –2 2 4 6 8 10

Example 3: Simplifying Before Solving Inequalities Page 25 Solve the inequality and graph the solutions: Multiply both sides by 6, the LCD of the fractions. Distribute 6 on the left side. 4f + 3 > 2 Since 3 is added to 4f, subtract 3 from both sides to undo the addition. –3 –3 4f > –1 Since f is multiplied by 4, divide both sides by 4 to undo the multiplication.

daily cost at We Got Wheels Example 4: Consumer Application Page 26 To rent a certain vehicle, Rent-A-Ride charges $55.00 per day with unlimited miles. The cost of renting a similar vehicle at We Got Wheels is $38.00 per day plus $0.20 per mile. For what number of miles in the cost at Rent-A-Ride less than the cost at We Got Wheels? Let m represent the number of miles. The cost for Rent-A-Ride should be less than that of We Got Wheels. Cost at Rent-A-Ride must be less than daily cost at We Got Wheels plus $0.20 per mile times # of miles. 55 < 38 + 0.20  m

Example 4 Continued 55 < 38 + 0.20m Since 38 is added to 0.20m, subtract 38 from both sides to undo the addition. –38 –38 55 < 38 + 0.20m 17 < 0.20m Since m is multiplied by 0.20, divide both sides by 0.20 to undo the multiplication. 85 < m Rent-A-Ride costs less when the number of miles is more than 85.

Classwork Assignment #5 Holt 3-4 #5, 12, 15