WhenToFlipAnInequality

1
When to flip the inequality
2
Rule
When multiplying or dividing an inequality by
a negative number, you must flip the inequality
symbol.
Why?
-5 -4 -3 -2 -1 0 1 2 3
4 5
Negative side
Positive side
Large is large
Large is small
3
Lets start at a basic level

• The whole point of inequalities is to find
  numbers that make TRUE STATEMENTS.

Do we flip when we add or subtract?
3 gt 2
1 1
4 gt 3
Large is still Large!
4
Lets start at a basic level

• The whole point of inequalities is to find
  numbers that make TRUE STATEMENTS.

Do we flip when we add or subtract?
3 gt 2
- 1 - 1
2 gt 1
Large is still Large!
5
Lets start at a basic level

• The whole point of inequalities is to find
  numbers that make TRUE STATEMENTS.

Do we flip when we add or subtract?
-3 lt -2
1 1
-2 lt -1
Large is still small!
6
Lets start at a basic level

• The whole point of inequalities is to find
  numbers that make TRUE STATEMENTS.

Do we flip when we add or subtract?
-3 lt -2
- 1 - 1
-4 lt -3
Large is still small!
7

• Adding and Subtracting from both sides require NO
  FLIPPING of signs

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Lets start at a basic level

• The whole point of inequalities is to find
  numbers that make TRUE STATEMENTS.

Do we flip when we multiply or divide by a
positive?
4 gt 2
x 2 x 2
8 gt 4
Large is still Large!
9
Lets start at a basic level

• The whole point of inequalities is to find
  numbers that make TRUE STATEMENTS.

Do we flip when we multiply or divide by a
positive?
-4 lt -2
x 2 x 2
-8 lt -4
Large is still small!
10
Lets start at a basic level

• The whole point of inequalities is to find
  numbers that make TRUE STATEMENTS.

Do we flip when we multiply or divide by a
positive?
4 gt 2
2 2
2 gt 1
Large is still Large!
11
Lets start at a basic level

• The whole point of inequalities is to find
  numbers that make TRUE STATEMENTS.

Do we flip when we multiply or divide by a
positive?
-4 lt -2
2 2
-2 lt -1
Large is still small!
12

• Multiplying and dividing by a positive () number
  requires NO FLIP because they cause true
  statements.

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Lets start at a basic level

• The whole point of inequalities is to find
  numbers that make TRUE STATEMENTS.

Do we flip when we multiply or divide by a
negative?
4 gt 2
x -2 x -2
-8 gt -4
UNTRUE
-8 lt -4
Flip to make true
14
Lets start at a basic level

• The whole point of inequalities is to find
  numbers that make TRUE STATEMENTS.

Do we flip when we multiply or divide by a
negative?
4 gt 2
-2 -2
-2 gt -1
UNTRUE
-2 lt -1
Flip to make true
15

• Multiplying and dividing by a negative () number
  requires A FLIP to make true statements

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Lets play a game
Should they have flipped it!
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1)
Use 0 and -1 to prove it
-1
0
0 lt 30
-5 lt 30
Both are still TRUE
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• Multiplying and dividing by a positive () number
  requires NO FLIP because they cause true
  statements.

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2)
Use -7 and -8 to prove it
-8
-7
35 lt 30
40 lt 30
BOTH are untrue!
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This way has to!
2)
This way doesnt work
Use 7 and 8 to prove it
7
8
-35 lt 30
-40 lt 30
BOTH are now TRUE
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• Multiplying and dividing by a negative () number
  requires A FLIP to make true statements

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Flip or not flip?
NO FLIP
FLIP
NO FLIP
NO FLIP
FLIP
FLIP
FLIP
NO FLIP
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Why do we flip these?
They require you to multiply by a negative to
solve. You have to flip them to make true
statements!
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Lets apply this rule to 2-step inequalities
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Flip or not flip?
NO FLIP
FLIP
NO FLIP
NO FLIP
FLIP
FLIP
NO FLIP
FLIP
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Why No Flip?

- 5 - 5
3 3
gt
Use 2 and 3 to prove
2
3
TRUE
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Why FLIP ?

- 6 - 6
gt
-2 -2
TRY -6
TRY 6
UNTRUE
TRUE
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First, tell me to flip or not to flip Second,
Solve inequality
FLIP
NO FLIP
FLIP
NO FLIP