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The set of elements that satisfies one statementand another statement.
Objective - To solve compound inequalities involving “and” and compound inequalities involving “or”.
Write a compound inequality that describes allthe real numbers greater than -2 and less than 5.
Conjunction - The intersection of two sets.
gx 2> − and x 5<
2 x 5− < < “In-between statement”
-3 -2 -1 0 1 2 3 4 5 6
-3 -2 -1 0 1 2 3 4 5 6
Write the following compound inequalities as “In Between” statements.
x 3 and x 5> − <1)
x 4 and x 10> <2)
3 x 5− < < 5 x 3> > −
x 4 and x 10> <2)
x 1 and x 8< − > −3)
4 x 10< <
8 x 1− < < −
Solve and graph the compound inequality.4 x 3 7− < + <
4 x 3 7− < + <4 x 3− < + and x 3 7+ <3 3− − 3 3− −
4 x 3 7− < + <3 3 3− − −
7 x 4− < <7 x− < x 4<
x 7> − and x 4<
7 x 4− < <-7 0 4
9 3x 3− < ≤3 3 3
Solve and graph.5 3x 4 7− < + ≤4 4 4− − −
3 1≤3 x 1− < ≤
-3 0 1
10 x 2− −
Solve and graph.4 6 x 8− ≤ − <6 6 6− − −10 x 2− ≤ − <
≥ >10 x 21 1 1− − −
-2 0 10
10 x 2≥ > −2 x 10− < ≤
≥ >
Disjunctions
Write a compound inequality that describes all real numbers less than -2 or greater than 5
The set of elements that satisfies one statement oranother statement.
Disjunction - The union of two sets.
all real numbers less than 2 or greater than 5.
x 2< − or x 5>
-3 -2 -1 0 1 2 3 4 5 6
Graph.
Lesson 3-6
Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010
Intersection vs. Union
Intersection Union“and” “or”
∩ ∪
Coke and Pepsi Coke or PepsiCoke and Pepsi Coke or Pepsi
coke pepsi coke pepsi
Coke ∩ Pepsi Coke ∪ Pepsi
2 2 4 4
Solve and graph the compound inequality.
2x 3 7− < 4x 7 33− ≥or3 3+ +
2x 10<
5
7 7+ +4x 40≥
10≥x 5< or x 10≥
x 5< or x 10≥
0 5 10
2x 24− −
5x 35−5 5− −
2 2
Solve and graph the compound inequality.5x 35− ≥ 1 2x 23− < −or
x 7≤ −
1 1− −2x 24− < −≤
>2 2− −x 7≤
or x 12>
-7 0 12
x 7≤ −x 12>
Number Line Graphs of InequalitiesIntersections Unions
x < 5 x < 3and x < 5 x < 3or0 1 2 3 4 5 6 0 1 2 3 4 5 6
{ x : x < 3 } { x : x < 5 }
x < 5 x > 3and0 1 2 3 4 5 6
{ x : 3 < x < 5 }
x < 5 x > 3or0 1 2 3 4 5 6
{ x : x = Any Real Number }
x > 5 x < 3and x > 5 x < 3or
{ } { x : x < 3 or x > 5 }
Intersections UnionsNumber Line Graphs of Inequalities
0 1 2 3 4 5 6 0 1 2 3 4 5 6
x > 5 x > 3and
{ x : x > 5 }
x > 5 x > 3or
{ x : x > 3 }
0 1 2 3 4 5 6 0 1 2 3 4 5 6
Lesson 3-6 (cont.)
Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010