Section 5.4 Day 1 Algebra 1

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”

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

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

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)

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

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

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

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

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

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

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