1. Objective
Solve inequalities that contain more than one operation.

2. Inequalities that contain more than one operation require more than one step to solve. Use inverse operations to undo the operations in the inequality one at a time.

3. 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

4. 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

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

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

7. Solve the inequality and graph the solutions.
Check It Out! Example 1c
Solve the inequality and graph the solutions.
1 – 2n ≥ 21
– –1
–2n ≥ 20
n ≤ –10
–10
–20
–12 –8 –4
–16

8. Example 2A: Simplifying Before Solving Inequalities
Solve the inequality and graph the solutions.
2 – (–10) > –4t
12 > –4t
–3 < t
(or t > –3) –3
–10 –8 –6 –4 –2 2 4 6 8 10

9. 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

10. Example 2C: Simplifying Before Solving Inequalities
Solve the inequality and graph the solutions.

11. Solve the inequality and graph the solutions.
Check It Out! Example 2a
Solve the inequality and graph the solutions.
2m + 5 > 52
2m + 5 > 25
– 5 > – 5
2m > 20
m > 10 2 4 6 8 10 12 14 16 18 20

12. Solve the inequality and graph the solutions.
Check It Out! Example 2b
Solve the inequality and graph the solutions.
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

13. Check It Out! Example 2c
Solve the inequality and graph the solutions.

14. daily cost at We Got Wheels
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.
Cost at Rent-A-Ride
must be less than
daily cost at We Got Wheels
plus
$0.20
per mile
times
# of miles.

15. is greater than or equal to
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.
First test score
plus
second test score
divided by
number of scores
is greater than or equal to
total score

16. Lesson Quiz: Part I
Solve each inequality and graph the solutions.
– 2x ≥ 21
x ≤ –4
2. – < 3p
p > –3
3. 23 < –2(3 – t)
t > 7 4.

17. Lesson Quiz: Part II
5. A video store has two movie rental plans. Plan A includes a $25 membership fee plus $1.25 for each movie rental. Plan B costs $40 for unlimited movie rentals. For what number of movie rentals is plan B less than plan A?
more than 12 movies