Algebra 1 10/17/16 EQ: How do I solve 2 and multi step inequalities? HW:pg. 159 # 17-37 odd, 50, 77-86 all Warm up: See hand out

Warm Up Solve each equation. 1. 2x – 5 = –17 2. –6 14 Solve each inequality and graph the solutions. 3. 5 < t + 9 t > –4 4. a ≤ –8

Additional Example 3: Application 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 is 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.

Additional Example 3 Continued –38 –38 55 < 38 + 0.20m 17 < 0.20m 85 < m Rent-A-Ride costs less when the number of miles is more than 85.

Check It Out! Example 3 The average of Jim’s two test scores must be at least 90 to make an A in the class. Jim got a 95 on his first test. What grades can Jim get on his second test to make an A in the class? Let x represent the test score needed. The average score is the sum of each score divided by 2.

Check It Out! Example 3 Continued –95 –95 x ≥ 85 The score on the second test must be 85 or higher.

Additional Example 1A: Solving Multi-Step Inequalities Solve the inequality and graph the solutions. 45 + 2b > 61 45 + 2b > 61 –45 –45 2b > 16 b > 8 2 4 6 8 10 12 14 16 18 20

Additional Example 1B: Solving Multi-Step Inequalities Solve the inequality and graph the solutions. 8 – 3y ≥ 29 8 – 3y ≥ 29 –8 –8 –3y ≥ 21 y ≤ –7 –10 –8 –6 –4 –2 2 4 6 8 10 –7

Solve the inequality and graph the solutions. Check your answer. Check It Out! Example 1a Solve the inequality and graph the solutions. Check your answer. –12 ≥ 3x + 6 –12 ≥ 3x + 6 – 6 – 6 –18 ≥ 3x –6 ≥ x –10 –8 –6 –4 –2 2 4 6 8 10

Solve the inequality and graph the solutions. Check your answer. Check It Out! Example 1b Solve the inequality and graph the solutions. Check your answer. –5 –5 x + 5 < –6 x < –11 –20 –12 –8 –4 –16 –11

Check It Out! Example 1c Solve the inequality and graph the solutions. Check your answer. 1 – 2n ≥ 21 –1 –1 –2n ≥ 20 n ≤ –10

Additional Example 2B: Simplifying Before Solving Inequalities Solve the inequality and graph the solutions. –4(2 – x) ≤ 8 −4(2 – x) ≤ 8 −4(2) − 4(−x) ≤ 8 –8 + 4x ≤ 8 +8 +8 4x ≤ 16 x ≤ 4 –10 –8 –6 –4 –2 2 4 6 8 10

Additional Example 2C: Simplifying Before Solving Inequalities Solve the inequality and graph the solutions. 4f + 3 > 2 –3 –3 4f > –1

Additional Example 2C Continued Solve the inequality and graph the solutions. 4f > –1

Solve the inequality and graph the solutions. Check your answer. Check It Out! Example 2b Solve the inequality and graph the solutions. Check your answer. 3 + 2(x + 4) > 3 3 + 2(x + 4) > 3 3 + 2x + 8 > 3 2x + 11 > 3 – 11 – 11 2x > –8 x > –4 –10 –8 –6 –4 –2 2 4 6 8 10