1. 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

2. Lesson 3.4 Solving Two-Step and multi-step Inequalities

3. Objectives
Solve inequalities that contain more than one operation

4. 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.

5. Steps to solve a Two-step inequality
Step 1: Undo addition or subtraction
Step 2: Undo multiplication and division
Is your variable isolated?

6. Subtracting a number is the same as adding its opposite.
7 – 2t = 7 + (–2t)
Remember!

7. Solving Multi-Step Inequalities
Solve the inequality and graph the solutions.
45 + 2b > 61
1. Add/ Subtract
45 + 2b > 61
– –45
2. Multiply/Divide
2b > 16
b > 8
The solution set is {b:b > 8}. 2 4 6 8 10 12 14 16 18 20

8. Solving Multi-Step Inequalities
Solve the inequality and graph the solutions.
8 – 3y ≥ 29
1. Add/Subtract
8 – 3y ≥ 29
– –8
2. Multiply/Divide
–3y ≥ 21
The solution set is {y:y  –7}.
y ≤ –7
–10 –8 –6 –4 –2 2 4 6 8 10 –7

9. The Box Method X < 4 Let’s try to solve backwards… 6x – 11 < 13
× 6
- 11 x ? 13
+ 11
÷ 6 13 4 24

10. You try
Solve and Graph the inequality

11. To solve more complicated inequalities, you may first need to simplify the expressions on one or both sides.

12. Simplifying Before Solving Inequalities
Solve the inequality and graph the solutions.
2 – (–10) > –4t
1. Combine like terms.
12 > –4t
2. Multiply/Divide
–3 < t
(or t > –3)
The solution set is {t:t > –3}. –3
–10 –8 –6 –4 –2 2 4 6 8 10

13. Simplifying Before Solving Inequalities
Solve the inequality and graph the solutions.
–4(2 – x) ≤ 8
1. Distributive Property
−4(2 – x) ≤ 8
−4(2) − 4(−x) ≤ 8
2. Add/Subtract
–8 + 4x ≤ 8
3. Multiply/Divide
4x ≤ 16
x ≤ 4
The solution set is {x:x ≤ 4}.
–10 –8 –6 –4 –2 2 4 6 8 10

14. is greater than or equal to
Word Problem
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 17
second test score
divided by
number of scores
is greater than or equal to
total score
(95 + x)  2 ≥ 90

15. Word Problem Continued
Since 95 + x is divided by 2, multiply both sides by 2 to undo the division.
95 + x ≥ 180
Since 95 is added to x, subtract 95 from both sides to undo the addition.
– –95
x ≥ 85
The score on the second test must be 85 or higher.

16. Now you try… 1. 3x – 7 > 2 4. x – 4 < 3 5 2. 4x + 1  -3

17. 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.

18. 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