Solving Inequalities Guided Lesson

Graphing and Solving Inequalities

LO

Labelling

Fill in the blank using the words provided

Drag labels to their correct position on the image

reversed

negative

variable

isolated

other side

inverse

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

Some text here about the topic of discussion

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!

​

Open Circle!​

​Graphing Inequalities

Some text here about the topic of discussion

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