Compound Inequalities and Interval Notation

Compound Inequalities and Interval Notation

by Katie Argall

​Goals for Today:

• ​Learn when to use compound inequalities

• ​How to write compound inequalities

• ​How to graph compound inequalities

• ​How to convert inequalities to interval notation

Multiple Choice

Identify a compound inequality 

• $$2<x<4$$  

• $$x<2$$  

• $$x>4$$  

• $$x<4\ and\ x\ >-2$$  

​Compound Inequalities

​Every day, the caretaker at the university’s biology lab checks

the water quality in the lab’s aquarium. The ideal pH level

recommended for freshwater aquariums is between 6.5 and 7.5.

How can the caretaker make a graph to show all the possible

values of the pH?

​

​

Multiple Choice

Select the correct inequality for the graph.

• -1 ≤ x < 6

• 1 ≤ x < 6

• 1 < x ≤ 6

• x ≤ 1 or x > 6

Multiple Choice

Every day, a man needs to eat more than 1800 but less than 1900 calories. Write an inequality representing the possible amount of calories you could get.

•  1800 ≤ c ≤ 1900

• 1800 ≤ c < 1900

• 1800 < c ≤ 1900

• 1800 < c < 1900

Multiple Choice

What inequality is graphed?

• 2 < x ≤ -3

• 2 < x < -3

• x > 2 or x ≤ -3

• x > 2 or x < -3

Multiple Choice

What inequality is graphed?

• x > 2 and x < 4

• 2 ≤ x ≤ 4

• x > 2 or x < 4

• x ≥ 2 or x ≤ 4

Multiple Choice

What inequality is graphed? 

• x > 2 and x ≤ -3

• x > 2 and x < -3

• x > 2 or x ≤ -3

• x > 2 or x < -3

​Solving Compound Inequalities "And"

Multiple Choice

-2 < x - 9 < 3

• x < 12

• 7 < x

• 7 < x < 12

• x > 7 or x < 12

​Solving inequalities "or"

​

Multiple Choice

$$x+2<-4\ \ \ \ \ or\ \ \ -5x<-15$$  

• -6<x<3

• x<-3 and x>6

• x<-6 or x>3

• No Solution

What is interval notation?

Multiple Choice

Write the following in interval notation

x > 6 and x ≤ 10

• (-∞, 6) and (10, ∞)

• [6, 10)

• (-∞, 6] and [10, ∞)

• (6, 10]

Multiple Choice

When writing a solution set in interval notation, what do I use for

< or > ?

• [ ]

• ( )

Multiple Choice

When writing a solution set in interval notation, what do I use for

≤ or ≥ ?

• [ ]

• ( )

Multiple Choice

Write the inequality in interval notation.

• [-4, -1)

• (-4, -1)

• (-4, -1]

• [-4, -1]

Multiple Choice

Can you use the symbols [ or ]

with infinity?

• Yes

• No

Multiple Choice

Which is the closest to the meaning of [a, b) ?

• All values between a and b, including both a and b

• All values between a and b, excluding both a and b

• All values between a and b, including a, but excluding b

• All values between a and b, including b, but excluding a