Inequalities

​Do you remember???

Multiple Choice

The sign below means... ≥

• Greater Than

• Less Than

• Greater Than or Equal to

• Less Than or Equal to

Multiple Choice

The sign below means... >

• Greater Than

• Less Than

• Greater Than or Equal to

• Less Than or Equal to

Multiple Choice

The sign below means... <

• Greater Than

• Less Than

• Greater Than or Equal to

• Less Than or Equal to

Multiple Choice

The sign below means... ≤

• Greater Than

• Less Than

• Greater Than or Equal to

• Less Than or Equal to

Multiple Choice

x is less than 9

• x < 9

• x > 9

• x ≥ 9

• x ≤ 9

Multiple Select

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

9 ___ -9

(Select all that apply.)

• >

• <

• ≥

• ≤

Multiple Choice

Is the statement true or false?

15 < -12

• True

• False

Multiple Choice

Is the statement true or false?

-17 > -18

• True

• False

Multiple Choice

Is the statement true or false. -6 > -5

• True

• False

Multiple Select

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

2 + 3 ____ -5

(Select all that apply.)

• >

• <

• ≥

• ≤

Multiple Choice

Which inequality symbol represents the statement. Less Than

• >

• ≤

• ≥

• <

Multiple Choice

Which inequality symbol represents the statement. Greater Than or Equal To

• >

• ≤

• ≥

• <

Multiple Choice

Which represents the word sentence as an inequality? A number w is smaller than -5.

• w < -5

• w > -5

• w ≤ -5

• w ≥ -5

Multiple Choice

x>5

• x is greater than 5

• x is less than 5

• x is zero

Multiple Choice

• less than

• greater than

• less than or equal to

• greater than or equal to

Multiple Select

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

-5 ____ -5

(Select all that apply.)

• >

• <

• ≥

• ≤

Multiple Choice

Write an inequality for this situation:  The restaurant can seat at most 172 people.

• x ≥ 172

• x ≤ 172

• x < 172

• x > 172

Multiple Choice

Write an inequality for this situation: All students in this class must get at least a 60% for the semester in order to pass their algebra class.

• x = 60

• x > 60

• x ≥ 60

• x ≤ 60

How are equations and inequalities different?

Equations

Have an = sign

Only have one answer when solved

Inequalities

Don't have and = sign instead use inequality symbols

< (less than)

> (greater than)

≤ (less than or equal to)

≥ (greater than or equal to)

Can have multiple answers when solved

Multiple Choice

Solve the following inequality:

x + 2 > 12

• subtract 2 from both sides and your answer is

  x = 10

• subtract 2 from both sides and your answer is

  x > 10

• subtract 2 from both sides and your answer is

  X < 10

Multiple Choice

Solve the inequality.

$$5>n-3$$  

• $$8<n$$  

• $$8>n$$  

• $$2>n$$  

• $$2<n$$  

Multiple Choice

8x ≥ -32

• x ≥ -4
• x ≥ 4
• x ≤ -4
• x ≥ 4

Multiple Choice

Solve 5x > 10

• divide by 5 on both sides and your answer is

  x = 2

• divide by 5 on both sides and your answer is

  x < 2

• divide by 5 on both sides and your answer is

  x > 2

Multiple Choice

Solve 3x + 2 > 8

• subtract 2 from both sides and your answer is

  x > 6

• subtract 2 from both sides and your answer is

  x = 6

• subtract 2 from both sides and then divide by 3 on both sides and your answer is

  x > 2

Multiple Choice

Solve the inequality

3x - 7 < 5

• x < 4

• x < -2

• x = 4

Multiple Choice

Solve. 3x + 2 > 14

• x > 4

• x > 36

• x > 5 1/3

• x > 48

Multiple Choice

-7 + 10z > -27

• z < -2

• z > -34

• 2 > z

• z > -2

One Rule: If you are multiplying or dividing by a negative number you must switch the direction of the inequality symbol. 

• (ex) Solve -4x > -12

• Divide both sides by -4, and because we are dividing by a negative number, we must reverse the inequality sign

  ⇒ -4x/-4 < -12/-4

  ⇒ x < 3

Multiple Select

When does the inequality sign change?

• When adding

• When multiplying

• When dividing by a negative

• When multiplying by a negative

• When subtracting

Multiple Choice

Do I need to flip my sign?
3x  ≥ 12

• Yes
• No

Multiple Choice

Do I need to flip my sign?
-2x  ≥ 14

• Yes
• No

Multiple Choice

Solve the inequality.

$$-7y\le14$$  

• $$y\le-2$$  

• $$y\ge-2$$  

• $$y\le2$$  

• $$y\ge2$$  

Multiple Choice

Solve:
5 - 3x < -4

• x > 3
• x < 3
• x < -3
• x > -3

Multiple Choice

-2x + 7 < 19

• x < 6
• x < -6
• x > 6
• x > -6

Multiple Choice

-3r + 10 < -2

• r < -8/3
• r > -8/3
• r > 4
• r < 4

Multiple Choice

Solve the inequality:

$$30-6x<6$$  

• $$x<-6$$  

• $$x>4$$  

• $$x<4$$  

• $$x>-6$$  

Multiple Choice

Solve:
2x + 5 <  3x - 6

• x < 11
• x > 11
• x > -11
• x < -11

Multiple Select

Which of the following are solutions to the inequality $$x>8$$  ? Select ALL of the correct answers.

• 6

• 7

• 9

• 10

Multiple Select

Which of the following are solutions to the inequality $$k\le15$$  ? Select ALL of the correct answers.

• 10

• 15

• 20

• 25

Multiple Select

Which of the following choices represents a solution to the given inequality?  

Note: There may be more than 1 correct choice. $$3x<12$$  

• $$x=0$$  

• $$x=8$$  

• $$x=-8$$  

• $$x=4$$  

• $$x=-4$$  

Match

Match the inequality statement with its symbol.

• $$>$$  

• $$\le$$  

• $$\ge$$  

• $$<$$   

greater than

no more than

at least

less than

• greater than

• no more than

• at least

• less than