1. Section 5.4 Day 1
Algebra 1

2. Learning targets Define & recognize a compound inequality
Graph a compound inequality containing the word “and”
Graph a compound inequality containing the word “or”
Solve a compound inequality containing the word “and”
Solve a compound inequality containing the word “or”

3. Compound Inequality
Case 1: “And”: only true if both inequalities are satisfied
Looking for the intersection of the inequalities
Case 2: “Or”: only true if at least one of the inequalities is true
Looking for the union of the inequalities

4. Intersection (And) Compound Inequality
Example 1:
Graph 𝑥≥3 and 𝑥<7
Can be re-written as 3≤𝑥<7

5. Intersection (And) Compound Inequality
Example 2:
Solve −2≤𝑥−3<4. Then, graph the solution set.
1. 1≤𝑥<7 (add 3 to both sides)

6. Intersection (And) Compound Inequality
Example 3:
Solve 𝑦−3≥−11 and 𝑦−3≤−8. Then graph the solution set.
1. 𝑦≥−8 and 𝑦≤−5 or −8≤𝑦≤−5. Need to add 3 to both inequalities

7. Intersection (And) Compound Inequality
Example 4:
Solve 6≤𝑟+7<10. Then, graph the solution set
1. −1≤𝑟<3. subtract 7 from each side

8. Union (OR) Compound Inequality
Example 5:
Graph 𝑥>2 or 𝑥≤−1

9. Union (OR) Compound Inequality
Example 6:
Solve −2𝑚+7≥13 or 5𝑚+12>37. Then graph the solution set
1. −2𝑚≥6 or 5𝑚>15
2. 𝑚≤−3 or 𝑚>3

10. Union (OR) Compound Inequality
Example 7:
Solve 𝑎+1<4 or 𝑎−1≥3. Then, graph the solution set
1. 𝑎<3 or 𝑎≥4

11. Union (OR) Compound Inequality
Example 8:
Solve 𝑥≤9 or 2+4𝑥<10. Then, graph the solution set
1. 𝑥≤9 or 4𝑥<8
2. 𝑥≤9 or 𝑥<4

12. Exit Ticket for Feedback
Solve and graph the following inequality
3𝑥+2≤11 or 5𝑥−8>22