Inequalities PreReq Review

Inequalities

What is an inequality?

LESS THAN

• is less than

• is fewer than

GREATER THAN

• is greater than

• is more than

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

Example of an inequality and how to interpret your answer.

Multiple Choice

WHICH SIGN GOES WITH THE PHRASE?

There are fewer than 50 people allowed in this area.

• $$<$$

• $$>$$

• $$\le$$

• $$\ge$$

Multiple Choice

WHICH SIGN GOES WITH THE PHRASE?

I need at least 30 orders to meet my qouta.

• $$<$$

• $$>$$

• $$\le$$

• $$\ge$$

Multiple Choice

WHICH SIGN GOES WITH THE PHRASE?

I see more than a dozen seagulls.

• $$<$$

• $$>$$

• $$\le$$

• $$\ge$$

Multiple Choice

WHICH SIGN GOES WITH THE PHRASE?

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

• $$<$$

• $$>$$

• $$\le$$

• $$\ge$$

SOLUTION OF AN INEQUALITY

• a value that makes an inequality true

• an inequality can have more than one solution

SOLUTION SET

• the set of all solutions of an inequality

Multiple Select

CHOOSE ALL VALUES OF X THAT ARE A SOLUTION OF THE INEQUALITY.

$$X<-5$$  

• -25

• 0

• -8

• -4

• -10

GRAPH OF AN INEQUALITY

Multiple Choice

Would x < 7 be a open or closed circle?

• open

• closed

To graph x > 5, draw an open circle at 5 on a number line.

• It is an open circle because <, > get open circles.

• ≤, ≥ get closed circles.

Multiple Choice

Would x < -10 be a open or closed circle?

• open

• closed

Multiple Choice

WHICH INEQUALITY IS REPRESENTED BY THE GRAPH?

• $$X\ <\ 1$$

• $$X\ \le\ 1$$

• $$X\ >\ 1$$

• $$X\ \ge\ 1$$

Multiple Choice

WHICH INEQUALITY IS REPRESENTED BY THE GRAPH?

• $$X\ <\ 2$$  

• $$X\ \ge\ 2$$  

• $$X\ >\ 2$$  

• $$X\ \le\ 2$$  

Multiple Choice

Which graph matches the inequality
2 > p?

• A
• B
• C
• D

Multiple Choice

Pick the correct inequality.

• A
• B
• C
• D

Multiple Choice

Which graph matches the inequality
-2 ≥ n?

• A
• B
• C
• D

How can you solve an inequality?

• An inequality uses <, >, ≤, ≥, and ≠ to compare two expressions.

• Inequalities have an infinite number of solutions.

• EXAMPLE: x > 5

• One solution is to use x = 7 because 7 > 5.

Solving Inequalities

• We solve inequalities the same way we solve equations.

• BUT THERE IS ONE DIFFERENCE THAT IS IMPORTANT!

• If you divide or multiply by a negative number you MUST flip the inequality sign.

Try to solve this on paper!

What would you do first?

What would you do second?

WHAT MUST YOU DO?

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

Solve the inequality:
$$4x-2<10$$  

• $$x>3$$  

• $$x<3$$  

• $$x>2$$  

• $$x<2$$  

Start at the open circle and color over the solutions you found. Draw an arrow to show that the solutions go on forever.

Open Ended

Name three solutions for z ≤ 11.

Multiple Choice

-7 + 10z > -27

• z < -2
• z > -34
• 2 > z
• z > -2

Multiple Choice

Solve and choose the correct graph:

• A
• B
• C
• D

Multiple Choice

Solve the inequality:

$$5y-11\ge9$$  

• $$y\le4$$  

• $$y\le-\frac{4}{11}$$  

• $$y\ge4$$  

• $$y\ge-\frac{4}{11}$$  

Multiple Choice

Solve 
-9h > (-63)

• h < 7
• h > 7
• h < -7
• h > -7

Multiple Choice

Solve the inequality:

$$-27-10x<23$$  

• $$x<5$$  

• $$x>5$$  

• $$x<-5$$  

• $$x>-5$$  

Multiple Choice

-4x + 14 ≤ 54

• x ≥ - 10

• x ≤ -10

• x ≥ 10

• x ≤ 10

Multiple Choice

When solving inequalities, when do you flip the inequality symbol?

• When the solution is a negative.

• When you multiply or divide both sides of the inequality by a negative number.

• When you multiply both sides of the inequality by any number.

• When you divide both sides of the inequality by a positive number.

Open Ended

Name three solutions for h > 8.

Multiple Choice

• x > 2
• x > 5
• x >15
• x > 50

Multiple Choice

Solve 

• a≤1
• a≤25
• a>1
• a<25

Multiple Choice

Which number line shows the solution to:
11x + 14 < –8? 

• a
• b
• c
• d

Multiple Choice

-8x < 48

• x < -6
• x > -6
• x < 6
• x > 6

Multiple Choice

Solve and graph the inequality.
7n - 1 > 76

• A
• B
• C
• D

Multiple Choice

- 2k > 18

• k is greater than 20
• k is less than negative 9
• k is greater than negative 9
• k is less than 36 

Multiple Choice

Solve and graph the inequality. $$-3\ge\frac{n}{3}-7$$

• A
• B
• C
• D

Multiple Choice

Does the sign need to flip when solving?
8y < (-40)

• YES
• NO

Multiple Choice

$$\frac{x}{4\ }\ -\ 2\ <13$$  

• x < 54
• x < 44
• x < 44
• x < 60

Multiple Choice

Solve

• x < -96
• x < 20
• x = 6
• x > 96

Multiple Choice

Solve for x.

$$\frac{x}{4}\ +\ 2\ \le\ 6$$  

• x ≥ 16

• x ≤ 16

• x ≥ 32

• x ≤ 32

Multiple Choice

-4 + y < -8

• y < 4
• y < -12
• y < -4
• y < 12

Multiple Choice

Solve for a.

-9a - 1 < 26

• a < -3

• a < 3

• a > -3

• a > 3

Multiple Choice

23 < f + 12

• f > 11

• f > 35

• f < 35

• f < 11

Multiple Choice

Which inequality represents six less than three times a number is at least fifteen?

• 3n - 6 < 15

• 3n - 6 > 15

• 3n - 6 < 15

• 3n - 6 > 15

Multiple Choice

You want to purchase a cell phone for $325.75 including tax. You have already saved $115 and can save $22 a week. Which inequality can be used to find the number of weeks it will take to save at least $325.75?

• 22w + 115 > 325.75

• 22w + 115 < 325.75

• 22 + 115w < 325.75

• 22w + 115 < 325.75

Challenge Questions

​Can you write an inequality?

Remember, we can use y=mx+b or ax+by=c, but we would also use the inequality symbol!

Multiple Choice

Ashley set a goal of saving a minimum of $200 in a savings account. She currently has $60 in the account. If she deposits $5 of her weekly allowance per week, how many weeks will it take her to reach her goal?

• x = Ashley

• x= her monthly allowance

• x = the number of weeks

• x = her savings account

Multiple Choice

Ashley set a goal of saving a minimum of $200 in a savings account. She currently has $60 in the account. If she deposits $5 of her weekly allowance per week, how many weeks will it take her to reach her goal?

• 60x + 5 > 200

• 5x + 60 > 200

• 5x + 60 < 200

• 60x + 5 < 200

Multiple Choice

Ashley set a goal of saving a minimum of $200 in a savings account. She currently has $60 in the account. If she deposits $5 of her weekly allowance per week, how many weeks will it take her to reach her goal?

• x > 28

• x < 28

• x > 28

• x < 28

Multiple Choice

Caleb is making lemonade and cookies for the school bake sale and he has 10 cups of sugar. The lemonade requires two cups of sugar and each batch of cookies uses 1 and 1/2 cups of sugar. What is the maximum number of batches of cookies he can make? Define the variable.

• x= cups of sugar

• x= lemonade

• x = cookie batches

• x = Caleb

Multiple Choice

Caleb is making lemonade and cookies for the school bake sale and he has 10 cups of sugar. The lemonade requires two cups of sugar and each batch of cookies uses 1 and 1/2 cups of sugar. What is the maximum number of batches of cookies he can make?

• 1.5x - 2 > 10

• 2x - 1.5 > 10

• 2x - 1.5 < 10

• 1.5x - 2 < 10

Multiple Choice

Caleb is making lemonade and cookies for the school bake sale and he has 10 cups of sugar. The lemonade requires two cups of sugar and each batch of cookies uses 1 and 1/2 cups of sugar. What is the maximum number of batches of cookies he can make?

• x > 8

• x < 8

• x < 8

• x > 8