Solving Inequalities

Graphing and Solving Inequalities

LO

Labeling

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other side

isolated

variable

inverse

reversed

negative

Match

Match the operation with its inverse (opposite) operation

• Addition

• Subtraction

• Multiplication

• Division

Subtraction

Addition

Division

Multiplication

• Subtraction

• Addition

• Division

• Multiplication

Direction of the arrow

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Multiple Choice

Which way will the arrow on the number line point?

$$x<-6$$  

• Left

• Right

Multiple Choice

Which way will the arrow on the number line point?

$$h\ge8$$  

• Left

• Right

Multiple Choice

Which way will the arrow on the number line point?

$$-3<f$$  

• Left

• Right

Closed Cirlce!

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Open Circle!​

​Graphing Inequalities

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Multiple Choice

Open dot or closed dot?

$$y\ge5$$  

• Open (not shaded) dot

• Closed (shaded) dot

Multiple Choice

Open dot or closed dot?

$$g<-14$$  

• Open (not shaded) dot

• Closed (Shaded) dot

Match

Rewrite the inequality to get the variable on the left side then match them together.

• 6 ≤ m

• 6 ≥ m

• 6 < m

• 6 > m

m ≥ 6

m ≤ 6

m > 6

m < 6

• m ≥ 6

• m ≤ 6

• m > 6

• m < 6

Multiple Choice

What operation is shown in the problem?


$$\frac{r}{7}\le15$$

• addition

• subtraction

• multiplication

• division

Multiple Choice

What would the inverse operation be?

$$\frac{r}{7}\ge15$$

• addition

• subtraction

• multiplication

• division

Multiple Choice

How do you solve this inequality:

x + 3 < 7

• Add 3 to both sides

• Divide both sides by 3

• Subtract 3 from both sides

• Multiply 3 to both sides.

Multiple Choice

How do you solve this inequality:

3y < 15

• Add 3 to both sides

• Divide both sides by 3

• Subtract 3 from both sides

• Multiply both sides by 3

Multiple Choice

1. n + 5 ≤ 16

• add 5 to one side

• subtract 5 from one side

• add 5 to both sides

• subtract 5 from both sides

Multiple Choice

1. n + 5 ≤ 16

   -5 -5

   What is the solution?

• n ≤ 11

• n ≥ 11

• n ≤ 21

• n ≤ -11

Multiple Choice

2. c - 9 > 14

What would you do to isolate the variable?

• add 9 to both sides

• subtract 9 from both sides

• add 14 to both sides

• subtract 14 from both sides

Multiple Choice

2. c - 9 > 14

+9 +9

What is the solution?

• c > 5

• c < 23

• c > 23

• c < 5

Multiple Choice

3. 12g < -48

   What would you do to both sides to isolate the variable?

• divide by -48

• multiply by -48

• divide by 12

• subtract 12

Multiple Choice

3. 12g ÷ 12 < -48 ÷ 12

After dividing both sides by 12 what is your solution?

• g > 4

• g < -4

• g < 4

• g > -4

When you multiply or divide both sides by a negative, you FLIP the inequality sign!

​Some text here about the topic of discussion.

​SPECIAL RULE

​Divide or multiply both sides of an inequality by a negative number, FLIP THE INEQUALITY SIGN.

Multiple Choice

When do you "flip" the inequality sign while you are solving inequalities?

• When you subtract from both sides

• When you multipy or divide both sides by a negative number

• When you add to both sides

Multiple Choice

Solve the inequality

-7x ≥ 35

Step 1: Use inverse option to isolate the variable

Step 2: When dividing or multiplying or dividing by a negative number you have to reverse the direction of the inequality symbol

• x ≥ -7

• x ≥ 7

• x ≤ -7

• x ≤ 7

Multiple Choice

x + 6.8 < 11.2

• x < 18

• x > 4.4

• x < 4.4

• x > 18

Poll

How do you feel about inequalites so far?

• I understand them

• I understand the inequality, but not the number line

• I need practice

• I don't understand

Multiple Choice

x - 5 > 16.7

• Subtract 5 from both sides to get

  x > 11.7

• Add 5 to both sides to get

  x > 21.7

Multiple Choice

x + 14 ≤ 16

• Add 14 to both sides to get

  x + 28 ≤ 40

• Add 14 to one side to get

  x + 14 ≤ 40

• subtract 14 from both sides to get

  x ≤ 2

• subtract 14 from one side to get

  x ≤ 16