Notes

1
Notes

• 8th Grade Math
• McDowell

Chapter 2
2
Graphing and Writing Inequalities 1/5

• Inequality signs

lt gt ³
Open dot Open dot Closed 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 gt 4
x is greater than 4
The variable comes first and we can use the chart
to graph
4 gt x
4 is greater than x
The variable does not come first
Flip the whole inequality around
x lt 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 gt -3? 5, 9, -2, or 37
Replace x with the possible solution and
determine if it is true.
5
Graphing Inequalities
Graph c gt -2.
gt 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 gt
Circle is over the -4
x gt -4.
7
You Try
Workbook p 35-36 all
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
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 gt 12

Example
x
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 gt 12
- 7
- 7
x
5
gt
11

• 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 all
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 lt 10

Example
a
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 lt 10
2 is positive so leave the inequality sign alone.
?2
?2
a
5
lt
15

• Solve m/-4 ? 3

Example
m
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 all
17
Solving Two-Step Equations 1/19

• Two-Step
• Equations

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
Firstundo any addition or subtraction
Secondundo any multiplication or division
20
Draw the road
Example
Work Backwards
Add 5 to both sides
-2x 5 25
5 5
Simplify

1. x
2. -2
3. ? -2
4. -5
5. 5

30
-2x
Divide both sides by -2
Simplify
-2
-2
x -15
Check your answer Plug and Chug
-2(-15) 5 25
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