Multi Step Inequalities

Inequalities

What is an inequality?

Inequality - Compares two values, showing if one is less than,
greater than, or simply not equal to another value.

17 > 12 17 is greater than 12

5 < 23 5 is less than 23

Inequalities

Symbol

Inequality

Graph

Greater than

>

x > -1

Reading and Writing Inequalities

1.

a < 24

“a is less than 24”

2.

c ≤ 13

3.

k ≥ -8

4.

7 > d

5.

-9 < m

6.

r ≤ 0

7.

w > 15

8.

-1 ≥ x

**Hint: Always read the variable first**

Understanding Inequalities

1.y < -3

a.-3

b.7

c.-9

d.10

e.-4

2.m ≥ 1

a.-1

b.1

c.-8

d.3

e.5

Directions: Select ALL answers that could be a value for the variable

3.8 < p

a.11

b.10

c.1

d.-4

e.8

4.k ≤ 4

a.0

b.-12

c.4

d.9

e.-4

5.b ≥ 0

a.-5

b.-3

c.0

d.3

e.4

6.-10 ≤ w

a.-11

b.3

c.6

d.0

e.-5

Graphing Inequalities

Open Circle
Greater than (>)

Less than (<)

Closed Circle
Greater than or equal to (≥)

Less than or equal to (≤)

Greater than

Greater than or equal to

Less than

Less than or equal to

When graphing inequalities you need to look at two things:
1. Open or Closed Circle
2. Direction of the arrow

**The direction of the arrow shows all the possible outcomes for the variable**

Graphing Inequalities

1.

7 > y

2.

m ≥ 25

3.

n > -4

4.

-1 ≥ f

Solving One-Step Inequalities

When solving inequalities, you solve the same way we did for solving algebraic equations.

1.

3y > 15

3. 24 ≥ x - 14

2.

2x ≥ 6

4. 15 < k + 32

Multiple Choice

Solve the following inequality:

x - 14 > 10

• x > 24

• x < 24

• x > -4

• x < -4

Solving Multi-Step Inequalities

When solving inequalities, you solve the same way we did for solving algebraic equations.

1.

2 + 5x > 57

3. -7 + 2n ≤ 5

2.

28 ≤ 4 + 3f

4. 38 > 6g + 2

Multiple Choice

Solve the following Inequality:

2x + 4 > 24

• x > 4

• x > 10

• x < 10

• x > 14

Solving and Graphing Inequalities

1.

5 + 3y ≤ 35

3. 6x + 3 > 69

2.

3r + 4 < -20

4. 4 ≤ 5 + d/4

Practice - Identify which problems should have
their sign flipped.

Should we flip the sign? YES or NO

1.

3y > 18 __________

5. 18 > -p __________

2.

-9n < 27 __________

6. h/-6 ≥ -18 __________

3.

24 ≥ k/-4 __________

7. -20 ≤ -3p + 4 __________

4.

12 < p/8 __________

8. 6c + 9 < 63 __________

Practice - Think whether to change the signs

1.

3y - 7 > 20

3.

2.

-8c + 4 ≤ 52

4.

Poll

How confident are you in your inequality knowledge and skills?

• I CAN TEACH THIS! I AM AN EXPERT!

• I got this! I feel okay!

• I want some more help, but I know I can do it.

• Oh no...... this is not for me at all #help

• What's an inequality?