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