1. Notes
8th Grade Math
McDowell
Chapter 2

2. Graphing and Writing Inequalities 1/5
Inequality signs
<
>
Open dot
Closed dot
less than
fewer than
greater than
more than
exceeds
less than or equal to
no more than
at most
greater than or equal to
no less than
at least

3. Order Matters
This chart only works if the variable comes first:
x > 4
x is greater than 4
The variable comes first and we can use the chart to graph
4 > x
4 is greater than x
The variable does not come first
Flip the whole inequality around
x < 4 is equivalent

4. Solution of An
Inequality
Any value that makes the inequality true
There can be infinity many solutions
Which are solutions of x > -3?
5, 9, -2, or –37
Replace x with the possible solution and determine if it is true.

5. ≤ Has a closed circle and points left
Graphing
Inequalities
Graph c > -2.
> Has an open circle and points right
Graph m ≤ 4.
≤ Has a closed circle and points left

6. Writing Inequalities from the graph
Write an inequality from each graph
Closed circle and points right ≤
Circle is over the 1
x ≤ 1
Open circle and points left >
Circle is over the -4
x > -4.

7. You Try
Workbook
p 35-36
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8. Solving Inequalities by Adding or Subtracting 1/6
The
Inequality
sign
When adding or subtracting, treat the inequality sign just like you would an = sign
Perform the inverse to isolate the variable and leave the inequality sign alone.

9. Ask three questions about the inequality:
Reminder
Ask three questions about the inequality:
1. What is the variable?
2. What operation is performed on the variable?
3. What is the inverse operation?
(The one that will undo what is being done to the variable)

10. Solve x + 7 > 12 Example x Addition. Subtraction. x + 7 > 12 - 7
1. What is the variable?
2. What operation is being performed on the variable?
Addition.
3. What is the inverse operation (the one that will undo what is being done to the variable)?
Subtraction.
The subtraction property of inequality tells us to subtract the same thing on both sides to keep the equation equal.
x + 7 > 12
- 7
- 7 x
> 5

11. Example y Subtraction. Addition. y – 10 ≤ -12 +10 +10 y ≤ -2
Solve y – 10 ≤ -12
Example y
1. What is the variable?
2. What operation is being performed on the variable?
Subtraction.
3. What is the inverse operation (the one that will undo what is being done to the variable)?
Addition.
The addition property of inequality tells us to add the same thing on both sides to keep the equation equal.
y – 10 ≤ -12
+10
+10 y ≤ -2

12. You Try
Workbook
p 37-38
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13. Solving Inequalities by Multiplying or Dividing 1/11
When multiplying or dividing on both sides of an inequality sign watch for negatives.
The
Inequality
sign
When multiplying or dividing by a positive number leave the inequality sign alone.
When multiplying or dividing by a negative number, flip the inequality sign.

14. Solve 2a < 10 Example a Multiply by 2 Divide by 2 2a < 10 2 2
1. What is the variable?
2. What operation is being performed on the variable?
Multiply by 2
3. What is the inverse operation (the one that will undo what is being done to the variable)?
Divide by 2
The division property of inequality tells us to divide the same thing on both sides to keep the equation equal.
2a < 10
2 is positive so leave the inequality sign alone. 2 2 a
< 5

15. Solve m/-4  3 Example m Divide by -4 Multiply by -4 m/-4  3 X-4 X-4
1. What is the variable?
2. What operation is being performed on the variable?
Divide by -4
3. What is the inverse operation (the one that will undo what is being done to the variable)?
Multiply by -4
The division property of inequality tells us to divide the same thing on both sides to keep the equation equal.
m/-4  3
-4 is negative so flip the inequality sign.
X-4
X-4 m 
-12

16. You Try
Workbook
p 39-40
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17. Solving Two-Step Equations 1/19
Two operations are required to isolate x
Plug and Chug to check your answer

18. Ask five questions about the inequality:
Solving Two Step Equations
1. What is the variable?
2. What is the first operation being done to the variable?
3. What is the inverse operation?
4. What is the second operation being done to the variable?
5. What is the inverse operation?

19. Work Backwards
First—undo any addition or subtraction
Second—undo any multiplication or division

20. Example -2x – 5 = 25 = 30 x = -15 -2(-15) – 5 = 25 30 – 5 = 25 25 = 25
Draw “the road”
Example
Work Backwards
-2x – 5 = 25
Add 5 to both sides
Simplify x
• -2
 -2 -5 +5
-2x
= 30
Divide both sides by -2 -2 -2
Simplify
x = -15
-2(-15) – 5 = 25
Check your answer
Plug and Chug
30 – 5 = 25
25 = 25

21. You Try
Solve
y – 4 = -12 2
2. –4m + 10 = 30
3. ¼a – 13 = -3

22. You Try
Workbook
p 113