Introduction to Inequalities

Introduction to Inequalities

By Omar Shishani

INEQUALITY

A mathematical sentence that compares expressions contains the symbols:

<, >, ≤, ≥

 

GREATER THAN

is greater than

is more than

LESS THAN

is less than

is fewer than

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

Which sign matches this phrase?

There are fewer than 50 people allowed in this area.

• x > 50

• x < 50

• x ≤ 50

• x ≥ 50

Multiple Choice

Which sign matches this phrase?

I need at least 30 orders to meet my goal.

• x > 30

• x < 30

• x ≤ 30

• x ≥ 30

Multiple Choice

Which sign matches this phrase?

I see more than 15 seagulls.

• x > 15

• x < 15

• x ≤ 15

• x ≥ 15

Multiple Choice

Which sign matches this phrase?

I can spend no more than $20 at the store.

• x > 20

• x < 20

• x ≤ 20

• x ≥ 20

Multiple Choice

What is this sign? $$\ne$$  

• Greater than

• Not Equal to

• Greater than or Equal to

• Less than or Equal to

SOLUTION OF INEQUALITY

A value that makes inequality true

Inequality can have more than one solution

What are the values of x?

Multiple Select

Choose all values of x that are a solution for the inequality.

X < 5

• 4

• 3

• 9

• 0

• -4

Multiple Select

Choose all values of x that are a solution for the inequality.

X ≤ -7

• -8

• -7

• 7

• -53

• -3

Multiple Select

Choose all values of x that are a solution for the inequality.

X ≥ -15

• -10

• -5

• 0

• 3

• -19

GRAPH OF INEQUALITY

Shows all the solutions of an inequality on a number line

Open circle is used when a number is not a solution < or >

Closed circle is used when a number is a solution ≤ or ≥

Multiple Choice

Which inequality is represented by the graph?

• x > 1

• x < 1

• x ≤ 1

• x ≥ 1

Multiple Choice

Which inequality is represented by the graph?

• x > 2

• x < 2

• x ≤ 2

• x ≥ 2