Introduction to Inequalities

4.4 : Inequalities

I can write and graph inequalities

Watch this BrainPop Video on Inequalities

Click here: https://www.youtube.com/watch?v=W87ymSALLiM

Inequality: a mathematical sentence that compares quantities that are NOT equal.

Notes:

What other words/ phrases could be represented by each symbol?

Multiple Choice

Choose an inequality.

My child's car seat can hold up to 50 pounds. Use c to represent the weight of the child allowed in the car seat.

• $$c<50$$

• $$c\le50$$

• $$c>50$$

• $$c\ge50$$

Multiple Choice

Choose an inequality.

You must be at least 48 inches tall to ride the roller coaster. Use h to represent your height. 

• $$h>48$$  

• $$h\ge48$$  

• $$h<48$$  

• $$h\le48$$  

Inequalities with variables are open sentences. When the variable in an open sentence is replaced with a number, the inequality may be true or false.

• If x=6, would this sentence be true?
  

•  $3x\le21$  
  

• What values for x would make this statement true?

Multiple Choice

Determine the truth of the inequality:  $$2t+8>7$$  when  $$t=1$$  

• True

• False

Multiple Choice

Determine the truth of the inequality:   $$p-42\le-2$$ when  $$p=40$$   

• True

• False

Multiple Choice

Determine the truth of the inequality:   $$y-7<10$$  when  $$y=10$$  

• True

• False

Notes: Inequalities can be graphed on a number line. The graph helps you visualize the values that make the inequality true.

Graphing Directions:

To determine the direction in which you should shade, choose a number to see if the value makes a true statement. Be sure to put an arrowhead on the end of the line.

Multiple Choice

$$x\le4$$  

Which graph matches this inequality?

Multiple Choice

$$y>2$$  

Which graph matches this inequality?

Multiple Choice

Which graph matches the inequality

r ≥ -6?

• A

• B

• C

• D

Notes:

Write an inequality to match the graph.

Multiple Choice

• x > 5

• x < 5

• x < 5

• x > 5

Multiple Choice

Match the graph with its inequality.

• 11 < a

• 11 > a

• 11 ≤ a

• 11 ≥ a

Practice!

Apply what we've learned about writing equations and inequalities

Multiple Choice

The maximum score on the pilot's test is 95 points.

• p < 95
• p > 95
• p ≥ 95
• p ≤ 95

Multiple Choice

A chef has 7 pounds of potatoes.  She needs more than 14 pounds for dinner.  What inequality describes the amount of potatoes the chef needs to buy?

• x - 7 > 14
• x + 7 > 14
• x - 7 < 14
• x + 7 < 14

Multiple Choice

Write an inequality for this situation:
You are driving, and the maximum speed limit is 55.

• s < 55
• s > 55
• s ≤ 55
• s ≥ 55

Multiple Choice

Melissa wants to spend no more than $300 on school clothes. She spends $75 on a coat and then wants to buy some sweaters that are on special for $10 each. Write an inequality to show how many sweaters Melissa can buy. DO NOT SOLVE

• 75x-10 ≥ 300
• 75+10 ≤ 300x
• 10x ≥ 300
• 75+10x ≤ 300

Multiple Choice

To order from the kids menu a person must be no more than 12 years old.

• x > 12
• x < 12
• x ≥ 12
• x  ≤ 12

Multiple Choice

A student must be at least 15 years old to obtain a driver’s permit.

• x > 15
• x < 15 
• x ≤ 15
• x ≥ 15

Multiple Choice

To qualify for an award, a student volunteers no less than 5 hours each week at the local hospital. Write an inequality that represents how many hours the student volunteers each week.

• X < 5
• X > 5
• X ≥ 5
• X ≤ 5

Multiple Choice

Match the scenario to the correct inequality

The distance from my mother to the remote control is less than 10 feet.

Use d to represent the distance in feet to the remote control

• $$d\ =10$$  

• $$d\le10$$  

• $$d\ \ge10$$  

• d < 10

Multiple Choice

Match the scenario to the correct inequality


It takes no less than two hours for Sharika's hair to dry
Use S to represent the amount of hours it takes for her hair to dry

• S $$\ge$$   2 
  

• S < 2

• S > 2

Multiple Choice

Match the sentence to  the correct inequality

The sum of a number times 3 and 15 is less than or equal to 32

• $$3\left(x\ +\ 15\right)\le32$$

• 3 ( x + 15) > 32

• $$3x\ +\ 15\ <32$$

• $$3x\ +15\ \le32$$

Multiple Choice

Match the sentence to the correct inequality.

The product of -6 and x is greater than or equal to 24

• $$\frac{-6}{x}\ge24$$

• $$-6\ +\ x\ \ge24$$

• $$24\ge-6x$$

• $$-6x\ge24$$

Multiple Choice

Match the inequality to the sentence below.

The sum of 7 and x is less than or equal to -20

• $$7x\le-20$$

• $$7-x\le-20$$

• $$7\ +\ x\le-20$$

• $$7\ +\ x\ =\ -20$$

Multiple Choice

Match the inequality to the sentence below.

14 is greater than t

• $$14<t$$

• $$t\le14$$

• $$14\ge t$$

• $$t<14$$

Homework:

ALEKS 4.4-4.5 Practice #1

Preview: Solving Inequalities

Watch this video: https://www.flocabulary.com/unit/inequalities/