Solving and Graphing Compound Linear Inequalities

3-6 Compound Inequalities

Page 200

10/22/20

A compound inequality consists of two distinct inequalities joined by the word and or the word or.

You can write a compound inequality involving and as a single inequality.

x > 4 and x < 9 can be written as

4 < x < 9

It can be read as x is between 4 and 9.

(not inclusive)

Problem 1 Got it? a

Write a compound inequality that represents the phrase and graph the solution.

All real numbers that are greater than or equal to -4 and less than 6.

Multiple Select

Choose all inequalities that represent the following phrase.

All real numbers that are greater than or equal to -4 and less than 6.

• $$-4<x\le6$$

• $$x\ge-4$$ and $$x<6$$

• $$-4\le x<6$$

• $$x>-4$$ or $$x<6$$

Multiple Choice

What did your graph look like?

Problem 1 Got it? b

Write a compound inequality that represents the phrase and graph the solution.

all real numbers that are less than or equal to 2.5 or greater than 6

Multiple Select

Choose all inequalities that represent the following phrase

all real numbers that are less than or equal to 2.5 or greater than 6

• $$x\le2\ \frac{1}{2}$$ or $$x>6$$

• $$2\ \frac{1}{2}\le\ x>6$$

• $$2\ \frac{1}{2}\le x<6$$

Multiple Choice

What does the graph look like?

$$x\le2\ \frac{1}{2}or\ x>6$$  

Multiple Choice

What inequality is being represented?

• 5<x<9

• 5≤x≤9

• 5<x≤9

• 5≤x<9

Multiple Choice

Which graph represents -2≤x≤3

• Graph 1

• Graph 2

• Graph 3

Multiple Choice

Which of the following is a compound inequality with "or"

Multiple Choice

Which graph represents x<-2 or x>3?

• Graph 1

• Graph 2

• Graph 3

Multiple Choice

$$-2<3y-4<14$$  How can you split up this inequality into two inequalities?

• $$-2<3y-4$$ and $$3y-4<14$$  

• You can't!

Multiple Select

How can you write the solutions to this inequality? $$-2<3y-4<14$$ Choose all! 

• $$\frac{2}{3}<y$$ and $$y<6$$  

• $$y>\frac{2}{3}\ and\ y<6$$  

• $$\frac{2}{3}<y<6$$  

Interval Notation

Interval notaion includes the use of three special symbols.

parenthesis: use ( or ) when the endpoints are not included

when you use < or > and graphs have open circles

brackets: Use [ or ] when endpoints are included

when you use or equal signs and graphs have closed circles

infinity:

use ∞ when the interval continues forever in a positive direction

use -∞ whenthe interval continues forever in a negative direction.

parenthesis are always used next to ∞ and -∞ never brackets!

Multiple Choice

When writing a solution in interval notation, what grouping symbol do I use for:

> or <

• [ ]

• ( )

Multiple Choice

When writing in interval notation, what kind of grouping symbol do I use for:

≤ or ≥

• [ ]

• ( )

Multiple Choice

What interval notation does the number line graph represent?

• [∞, -5)

• (∞, -5)

• [-5, ∞)

• (-5, ∞)

Multiple Choice

Can you use the symbols [ or ]
with infinity?

• Yes
• No

Multiple Choice

Look at the graph. Write the interval notation for the graph.

• (-2,5)

• (-∞,-2) or (5,∞)

• [-2,5]

• (-∞,-2]∪[5,∞)

Multiple Choice

Write the following in interval notation

x < 8

• [8, ∞)

• (8, -∞)

• (-∞, 8]

• (-∞, 8)

Multiple Choice

Write the interval notation for the graph?

• [-3, 2)

• -3<x<2

• (-∞, -3] or (2, ∞)

• x > 2 or x < -3

Multiple Choice

Write the inequality in interval notation.

• [-4, -1)

• (-4, -1)

• (-4, -1]

• [-4, -1]

Multiple Choice

Solve the compound inequality:

-3 ≤ 2x - 1 ≤ 5

• -1 ≤ x ≤ 3

• -1 < x < 3

• 1 < x < 3

• 1 ≤ x ≤ 3

Multiple Choice

Solve the compound inequality

3x-4 < -13 or 7x+1 > 22

• All Real numbers

• x > 3 AND x > -9

• The answer is not listed

• x < -3 OR x > 3