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

2. 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

3. 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.

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

5. 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.

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

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

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

9. 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
–18 ≥ 3x
–6 ≥ x
–10 –8 –6 –4 –2 2 4 6 8 10

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

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

12. 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
4x ≤ 16
x ≤ 4
–10 –8 –6 –4 –2 2 4 6 8 10

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

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

15. 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