1. 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

2. 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
–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

3. 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
–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

4. 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
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

5. 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.

6. 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

7. Example 4 Continued
55 < m
Since 38 is added to 0.20m, subtract 38 from both sides to undo the addition.
–38 –38
55 < m
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.

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