1. Lesson 2-6: Compound Inequalities
Objective
Students will solve and graph conjunctions and disjunctions of inequalities

2. Read “x values such that x is…
Conjunction and Intersection
Connected with word “and”
Think “in common” or “overlap”
Common elements are the intersection of two sets
Symbol:
Read “x values such that x is…
Example 1: Find A B
Set A = { x | x < 5 } and B = { x | x > -1}
Or ( -1, 5 ]

3. Disjunction and Union Connected with word “or”
Think “both” or “put together”
Common elements are the union of two sets
Symbol:
Example 2: Find A B
Set A = { x | x > 3 } or B = { x | x < -2}
= {x | x < -2 or x > 3} or

4. Other Possible Solutions:
Combination of inequalities/graphs
Ex 3: x > -2 or x < 5
Any real number makes one or the other true so…
All real numbers or R or
Ex 4: x < - 4 and x > -1
There is no number that makes both true so ….
Empty Set or ø

5. Solve means: Find the values that make it true
Ex 5: -2x +4 ≤ -3 or x + 5 < 3
-2x ≤ x < -2
x ≥
So {x x < -2 or x ≥ } or