Solving Inequalities

Introduction to Inequalities

This truck is demonstrating a lack of inequality knowledge! He was taller than the maximum height!

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We use inequalities often in practical situations​, without even realizing it!

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why do inequalities matter?

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Multiple Choice

What is this symbol?

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

Multiple Choice

What is this symbol?

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

Multiple Choice

Greater than

• <
• >
• ≤
• ≥

Multiple Choice

Less Than

• <
• >
• ≤
• ≥

Multiple Choice

$$x\ge6$$   How do you read this inequality?

• x is less than or equal to 6

• x is greater than or equal to 6

• x is less than 6

• x is greater than 6

Multiple Choice

Is x = 9 a solution to the given inequality.
x > 9

• TRUE
• FALSE

Multiple Select

Select all of the following that are solutions to the inequality  $$5<x$$  ?

• 3

• 6

• 8

• 10

Multiple Select

Select ALL of the following that are solutions to the inequality $$x>8$$  ?

• 6

• 7

• 9

• 10

Multiple Select

Select ALL of the following that are solutions to the inequality $$k\le15$$  ?

• 10

• 15

• 20

• 25

Multiple Choice

Is $$b=6$$  a solution to the inequality  $$b-3>5$$  ?

• Yes

• No

Multiple Choice

Does the given value make the inequality true?  x + 9 > 21, when x = 15

• Yes, it is a solution.
• No, it is not a solution.

Multiple Choice

$$2\left(x-3\right)+9\ge x$$  

• $$x\ge-6$$  

• $$x\ge15$$  

• $$x\le-3$$  

• $$x\ge-3$$  

• $$x\le-6$$  

Multiple Choice

Solve the following Inequality 

$$-3\left(b+5\right)<45$$  

• $$b>-20$$  

• $$b>-10$$  

• $$b<-20$$  

• $$b<-10$$  

• $$b>-\frac{40}{3}$$  

Fill in the Blank

Would the inequality sign flip? (Type Yes or No) $$-2x\ +3<\ 8$$  

Multiple Choice

Solve the inequality.
x + 5 ≤ 13

• x ≥ 8
• x ≥ 18
• x ≤ 8 
• x ≤ 18 

Multiple Choice

Solve the inequality.
30 + n ≥ 50

• x > 50
• x > 80
• x < 30
• x > 20

Multiple Choice

You flip an inequality symbol when you...

• subtract
• multiply and divide only
• multiple by a negative number
• multiple or divide by a negative number

Multiple Choice

-8x < 48

• x < -6

• x > -6

• x < 6

• x > 6

Multiple Choice

You try!

Solve. $$1-3x\ +6x>10-6x$$  

• x > 1

• x < -1

• x > 9

• x < 9

Multiple Choice

7b - 3 < 11

• b < 2
• 84 > b
• b > 2
• b < 84

Multiple Choice

4x + 1 > 13

• x > 48
• x < 3
• x > 3.5
• x > 3

Multiple Choice

10 ≥ x - 3

• x ≤ 13
• x ≥ 13
• x ≤ 7
• x ≥ 7

Multiple Choice

Solve the following inequality. Show your algebraic work!

• b > 6

• b < -4

• b > 1

• b < -12

Multiple Choice

6x - 4 ≥ 26

• x ≥ 3.67
• x ≥ 5
• x < 5
• x ≤ 5

Multiple Choice

Solve the inequality.

$$2\left(b\ -\ 8\right)\ >\ 12$$  

• b > 20

• b > 6

• b > 14

• b > 20

Multiple Choice

Solve the inequality.

$$-4d\ -\ 9\ \le\ 3$$  

• $$d\ \le3$$  

• $$d\ \le-3$$  

• $$d\ \ge\ 3$$  

• $$d\ \ge\ -3$$  

Multiple Choice

Solve
-5m < 10

• m < -2
• m > -2
• m < -50
• m > -50

Multiple Choice

$$6x>12$$  

• $$x<2$$  

• $$x\le2$$  

• $$x>2$$  

• $$x\ge2$$  

Multiple Choice

$$\frac{b}{2}<13$$  

• $$b<26$$  

• $$b\le26$$  

• $$b>26$$  

• $$b\ge26$$  

Multiple Choice

x - 3<10

• x > 13

• x <13

• x ≤ 7
• x ≥ 7