Day 4 - Solving Linear Inequalities

Bell Ringer

“The ability to concentrate and to use your

time well is everything if you want to succeed
in business- or almost anywhere else for that

matter.”

~Lee Iacocca

Bell Ringer:
Write the inequality that represent the scenario.

Scenarios

1. The room holds no more than 400 people.
2. Steve runs more than 40 miles per week.
3. Michael needs at least an 80% on his test.
4. Ms. Newkirk only has $20 to spend.
5. Sally needs 15 more votes to win.
6. The elevator holds a maximum of 700 pounds.
7. There must be no more than 10 people on the court.
8. She needs at least 25 cupcakes for the party.
9. His age is less than his height.

10.The ballroom has a capacity of 200 people.

Multiple Choice

The room holds no more than 400 people. Which inequality represents the amount of people the room holds?

• P ≥ 400

• P ≤ 400

• P < 400

• P > 400

Multiple Choice

Steve runs more than 40 miles per week. Which inequality represents the amount of miles he runs?

• M < 40

• M ≥ 40

• M ≤ 40

• M > 40

Multiple Choice

Michael needs at least an 80% on his test. Which inequality represents the grade that Michael can get on his test?

• P ≥ 80

• P < 80

• P > 80

• P ≤ 80

Multiple Choice

Ms. Newkirk only has $20 to spend. Which inequality represents the amount which Ms. Newkirk can spend?

• M > 20
• M ≤ 20
• M < 20
• M ≥ 20

Multiple Choice

Sally needs 15 more votes to win. Which inequality represents the numbers of votes Sally needs?

• V < 15

• V > 15

• V ≥ 15

• V ≤ 15

Multiple Choice

The elevator holds a maximum of 700 pounds. Which inequality represents the amount of pounds the elevator can hold?

• P < 700

• P ≤ 700

• P > 700

• P ≥ 700

Multiple Choice

There must be no more than 10 people on the court. Which inequality describes the situation?

• x > 10

• x < 10

• x ⪯ 10

• x ⪰ 10

Multiple Choice

She needs at least 25 cupcakes for the party.  Which inequality describes the situation?

• x > 25

• x < 25

• x ⪯ 25

• x ⪰ 25

Multiple Choice

His age is less than his height. Which inequality describes the situation?

• a > h

• a < h

• a ⪯ h

• a ⪰ h

Multiple Choice

Which inequality represents the following sentence: The ballroom has a capacity of 200 people.

• x > 200

• x < 200

• x ⪰ 200

• x ⪯ 200

Learning Target(s):

I will

❖ Solve and graph a linear inequality
❖ Justify the steps for solving a linear inequalities
❖ Create and solve an inequalities from a context

Standard: MGSE9-12.A.REI.1, 3

Success Criteria :

I can
● Write and solve one-step and multistep inequalities consisting of all

rational numbers.

● Understand the difference between an equations and an inequalities.

Standard:MGSE9-12.A.REI.1, 3

ANINEQUALITYISASTATEMENTTHATTHATCOMPARESTWO

QUANTITIES. THEQUANTITIESBEINGCOMPAREDUSEONEOF

THEFOLLOWINGSIGNS:

When reading an inequality, you always to want to read from the variable. Translate the inequalities into words:
A. x > 2

B. -3 > p

C. y ≤ 0

D. -2 ≤ z

E. x ≠ 1

_____________________

_____________________

_____________________

_____________________

_____________________

Draw

When reading an inequality, you always to want to read from the variable. Translate the inequalities into words:

x > 2

Draw

When reading an inequality, you always to want to read from the variable. Translate the inequalities into words:

-3 > p

Draw

When reading an inequality, you always to want to read from the variable. Translate the inequalities into words:

y ≤ 0

Draw

When reading an inequality, you always to want to read from the variable. Translate the inequalities into words:

-2 ≤ z

Draw

When reading an inequality, you always to want to read from the variable. Translate the inequalities into words:

x ≠ 1

Inequalities are similar to equations
when solving. You can add, subtract,
multiply or divide any amount to either side as long as you do it to both sides.

INEQUALITIES

NEGATIVE PROPERTYOF INEQUALITY

If numbers are not equal to the same
number, but get affected by a negative
then the sign must change.

● If a > b, then -a < -b.
● If a < b, then -a > -b.

● Ex: 5 > 2, so -5 < -2

NEGATIVE MULTIPLICATION PROPERTYOF INEQUALITY
Multiplying both sides of the inequality
by the same negative number, other than
0, does change the inequality.

● If a > b, then -ac < -bc.
● If a < b, then -ac > -bc.

● Ex: x > y, so -3x < -3y

NEGATIVE DIVISION PROPERTYOF INEQUALITY
Dividing both sides of the equation by the
same number, other than 0, does change the
inequality.

● If a > b, then a/-c < b/-c.

● If a < b, then a/-c > b/-c.

● Ex: x > y, so x/-7 < y/-7

Match

Match the following

• Addition property of inequality

• Subtraction property of inequality

• Symmetric property of inequality

• Transitive property of inequality

• Negative property of inequality

If a > b, then a + c > b + c.

If a > b, then a - c > b - c.

If a > b, then b < a.

If a > b and b > c, then a > c.

If a > b, then –a < – b.

• If a > b, then a + c > b + c.

• If a > b, then a - c > b - c.

• If a > b, then b < a.

• If a > b and b > c, then a > c.

• If a > b, then –a < – b.

Match

Match the following

• If a > b, then –a < – b.

• If a > b and c > 0, then a • c > b • c.

• If a > b and c < 0, then a ÷ c < b ÷ c.

• If a > b and c < 0, then a • c < b • c.

• If a > b and c > 0, then a ÷ c > b ÷ c.

Negative property of inequality

Multiplication property of inequality

Negative Division property of inequality

Negative Multiplication property of inequality

Division property of inequality

• Negative property of inequality

• Multiplication property of inequality

• Negative Division property of inequality

• Negative Multiplication property of inequality

• Division property of inequality

Do you change the sign if you multiply or
divide by a positive number while solving?

NO!!!!

When you multiply or divide each side of an inequality by a negative integer, you must reverse the inequality symbol.

RECAP: DO YOU CHANGE THE SIGN?

Multiple Choice

When do we have to FLIP the sign in an inequality?

• when we add or subtract a negative number on both sides

• when we multiply both sides by a negative number, ONLY

• when we divide both sides by a negative number, ONLY

• when we multiply OR divide both sides by a negative number

Multiple Choice

Do you change the sign?

-15 $$\le$$ 5a

• yes

• no

Multiple Choice

Do you change the sign?

$$\frac{y}{4}$$ $$>$$ -20

• yes

• no

Multiple Choice

Do you change the sign?

-3m < -33

• yes

• no

SOLVING ONE VARIABLE

INEQUALITIES

≥

<

>

≤

Less than or equal to

Greater than

Greater than or equal to

Less than

Solving Inequalities

Addition Property for Inequalities

X-15<73

X-15+15<73+15

X<88

Add 15 to
both sides

Solving Inequalities

Subtraction Property for Inequalities

y+15<25

y+15-15<25-15

y<10

Subtract 15 from
both sides

Solving Inequalities

Division Property for Inequalities

Divide both sides by
the coefficient of x

Division Property for Inequalities

Caution! Dividing by a

negative number

Notice: Sign
CHANGED

Same if multiplying?

Multiplication Property for Inequalities

Caution! When you multiply

by a negative number…

…the sign
CHANGES

YES!
-x > 2

5

x < -10

(-5 )-x > 2(-5)

5

Multiple Choice

Is the statement below TRUE or FALSE?

13 > 13

• TRUE

• FALSE

Multiple Choice

Which of the following integers is a solution to the inequality below?

x < -5

• -6

• -5

• -4

Multiple Choice

Given the inequality x > 7, what is the smallest possible value of x in the solution set?

• 7

• 8

Multiple Choice

Given the inequality x > 20, what is the smallest integer value of x in the solution set?

• 20.1

• 20.01

• 20.001

• 21

Multiple Choice

-13t > 26

• t > -2

• t > 2

• t < 2

• t < -2

Multiple Choice

-7 + 10z > -27

• z < -2

• z > -34

• 2 > z

• z > -2

Multiple Choice

Solve:
6x+10>5x-12

• x>2

• x<2

• x<-22

• x>-22

Multiple Choice

X + 6 > 10

• X > 16

• X > -4

• X < -4

• X > 4

Multiple Choice

-7x + 15 ≥ -20

• x ≥ -5

• x ≤ -5

• x ≥ 5

• x ≤ 5

Multiple Choice

3(x-2)<2(x+9)

• x<24

• x>-24

• x<12

• x>18

Multiple Choice

10 ≥ x - 3

• x ≤ 13

• x ≥ 13

• x ≤ 7

• x ≥ 7

Multiple Choice

Solve the inequality. Don't forget to check your solution set.
12 ≥ 15 - 6y

• y ≤ ½

• y ≤ 2

• y ≥ ½

• y ≥ 2

Multiple Choice

-3 − 6(4x + 6) > -111

• x > 3

• x < 3

• x < -3

• x > -3

Multiple Choice

Which is a solution of

5(2v + 3) - 10v > -10

• no solution

• v > 5

• v > -5

• all real numbers

Multiple Select

Select all values that are solutions to the inequality x < 20

• 0

• 100

• 10

• 50

Multiple Select

Which value(s) make the inequality true?   x $$\ge$$  14. Choose more than one answer.

• 5

• 12

• 17

• 21

Multiple Choice

Solve the inequality:

3(x – 1) ≥ –9

• x ≥ –2

• x ≥ 2

• x ≤ –2

• x ≤ 2

Multiple Choice

Solve the inequality: $$6x-\left(2x-3\right)\le7+2x$$  

• $$$$  

• $$x\le2$$  

• $$x\le-1$$  

• $$$$  

Multiple Choice

Solve the inequality: $$2\left(x-8\right)+7<-5\left(x+2\right)-3x-19$$  

• $$x<-2$$  

• $$x>-2$$  

• $$x<2$$  

• $$x\le-2$$  

Multiple Choice

Which value is a solution to 5x - 3 > 24?

• 4

• 6

• 5

• 3

Multiple Choice

Which value is a solution to 2x - 5 $$\le$$  18?

• 30

• 25

• 24

• 10

IXL Quiz: Solving Linear Inequalities