Introduction to Inequalities

Introduction to Inequalities

Identifying and Graphing Inequalities

​Dr. Tom Giles

INEQUALITY

Greater Than ( > )

• is greater than

• is more than

• mas grande que

Less than ( < )

• is less than

• is fewer than

• menos que

Greater Than or Equal To

• is greater than or equal to

• is at least

• is no less than

Less Than Or Equal To

• is less than or equal to

• is at most

• is no more than

Multiple Choice

What symbol could go in the box to make a true statement?
71  ___  2

• >
• <
• ≥
• ≤

Multiple Choice

Less Than

• <

• >

• ≤

• ≥

Multiple Choice

Which inequality symbol is being shown in the picture?

• greater than

• less than

• less than or equal to

• greater than or equal to

Multiple Choice

• less than
• greater than
• less than or equal to
• greater than or equal to

Solution (answer) of an Inequality

• a value that makes the inequality true

• an inequality can have MORE THAN ONE solution

Multiple Choice

Is 4 a possible solution for p ≥ -8 ?

• Yes
• No

Multiple Choice

Is 9 a possible solution for k<7 ?

• Yes
• No

Multiple Select

Choose ALL the values that are a solution to x $$\le$$  4 

• -2

• 0

• 4

• 6

• 14

Graph of an inequality

Multiple Select

Which inequality symbol(s) has a graph with an OPEN circle?

• <

• ≤

• >

• $$\ge$$  

Multiple Choice

Would you use a closed or open circle to graph x < 3?

• Closed
• Open

Multiple Choice

Match the graph with its inequality.

• c > 9
• c < 9
• c ≥ 9
• c ≤ 9

Multiple Choice

Match the graph with its inequality.

• a > 11

• a < 11

• a ≥ 11

• a ≤ 11

Two-Variable Inequalities

Match

Match each phrase with the correct symbol.

• $$>$$  

• $$\ge$$  

• $$\le$$  

• $$<$$  

• $$\ne$$  

greater than

greater than or equal to

less than or equal to

less than

not equal to

• greater than

• greater than or equal to

• less than or equal to

• less than

• not equal to

Multiple Choice

What is the solution to a system of EQUATIONS?

• Intersection

• Overlapping Region

​ Two-Variable Inequalties

Multiple Choice

What is the solution to the inequality:

$$y\ge\frac{3}{4}x+3$$  

Multiple Choice

Write the inequality represented by the graph:

• $$y\le-\left(x+1\right)^2+4$$

• $$y<-\left(x+1\right)^2+4$$

• $$y>-\left(x+1\right)^2+4$$

• $$y\ge-\left(x+1\right)^2+4$$

Fill in the Blanks

Write the inequality represented by the graph. (Use no spaces)

Multiple Choice

Which of the following inequalities matches the graph?

• y < -4x - 1

• y < -(1/4)x - 1

• y < 4x - 1

• y < -4x - 1

Multiple Choice

Which of the following inequalities matches the graph?

• 4y + 3x < 20

• 4y - 3x < 20

• 4y + 3x > 20

• 4y - 3x > 20

Multiple Choice

Which of the following inequalities matches the graph?

• -2y > 2x - 2

• -2y > -4x + 4

• -2y < -4x + 4

• -2y ≤ 2x - 2

Multiple Choice

Which of the following inequalities matches the graph?

• y > x + 2

• y < -x + 2

• y < 2x + 2

• y < x + 2

Multiple Choice

Which of the following inequalities matches the graph?

• 4x > -2

• 4x < -8

• 4y > -8

• 4y < -2

Multiple Choice

Select the correct graph for each inequality.

• A

• B

• C

• _D

Multiple Choice

Which point below is NOT part of the solution set?

• (0, -2)
• (1, 1)
• (3, 3)
• (2, 10)

Multiple Choice

Which point below is NOT part of the solution set?

• (3, 4)
• (0, 4)
• (-2, 6)
• (6, 2)

Multiple Choice

Which of the following inequalities matches the graph?

• y < -4x - 1
• y > -4x - 1
• y ≤ -4x - 1
• y ≥ -4x - 1

Multiple Choice

Which of the following inequalities matches the graph?

• y ≤ 3/4x + 5
• y ≥ 3/4x + 5
• y < 3/4x + 5
• y > 3/4x + 5

Multiple Choice

Which of the following inequalities matches the graph?

• y ≥ x + 2
• y ≤ x + 2
• y > x + 2
• y < x + 2

Poll

Rate yourself on your understanding of today's topic

• Not a clue. See you at office hours.

• Starting to get the hang of this

• Overall I think I'm getting it, still making some mistakes

• A+ here I come!

Multiple Choice

What is the solution to the inequality:

$$y>\left|x-1\right|-2$$