Inequalities ppt revised
Transcript of Inequalities ppt revised
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INEQUALITIES
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Equal or Unequal?
• We call a math statement an EQUATION when both sides of the statement are equal to each other.– Example: 10 = 5 + 3 + 2
• We call a math statement an INEQUALITY when both sides of the statement are not equal to each other.– Example: 10 = 5 + 5 + 5
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Inequality Signs
• We don’t use the = sign if both sides of the statement are not equal, we use other signs.
GREATER THAN GREATER THAN (OR EQUAL TO)
LESS THAN LESS THAN (OR EQUAL TO)
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DON’T FORGET THIS!!!
• THE BIGGER SIDE OF THE SIGN IS ON THE SAME SIDE AS THE BIGGER #
• THE SMALLER SIDE OF THE SIGN IS ON THE SAME SIDE AS THE SMALLER #
– Examples: 10 15 or -4 -12< >
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Let’s Try Some!
• 3 5
• 22 10
• -10 4
• 2 7
• -65 -62
• 32.332.5
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Our Friend, The Number Line
• A number line is simply this…
…a line with numbers on it.
• We use a number line to count and to graphically show numbers.– Example: Graph x = 5.
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Graphing Inequalities
• Graph x = 2
• Graph x < 2
• Graph x < 2
• Graph x > 2
• Graph x > 2
A “closed” circle ( )indicates we includethe number.
An “open” circle ( )indicates we DO NOTinclude the number.
By shading in the number line we areindicating that all thenumbers in the shadeare also possible answers.
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You Try This…
• Graph x < 10
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You Try This…
• Graph x > -4
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You Try This…
• Graph x > 200
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You Try This…
• Graph x ≥ 7
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Write the following inequalities:5. Seven is less than or equal to three less than two times a number.
7 ≤ 2x – 3 6. The sum of two numbers is greater than
six less than the first number.
x + y > x - 67. Eleven more than a number, divided by
five is less than eighteen.x + 11 < 18
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Let’s Go Shopping!
• Last week you went shopping at the mall. You had $150 to spend for the day. You bought a shirt for $25 and some jeans for $40. You also spent $5 on lunch. You wanted to purchase a pair of shoes. What is the maximum amount of money you could have spent on the shoes?
The maximum amount you have
The amount youhave spent
The cost ofthe shoes
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How much can the shoes cost?
• Basically, the shoes must cost less than or equal to the amount you have left!
$25 + $40 + $5 + x ≤ $150$70 + x ≤ $150 -$70 -$70
X ≤ $ 80The cost ofthe shoes
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Do You Really Understand?
• Let’s see if this makes sense…
(If we add 6 to both sides, is the inequality true?)
3 < 9
3+6 < 9+6
9 < 15
YES!
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Do You Really Understand?
• Let’s see if this really makes sense…
(If we subtract 3 from both sides, is the inequality true?)
10 > 4
10-3 > 4-3
7 > 1
YES!
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Do You Really Understand?
• Let’s see if this still really makes sense…
(If we multiply both sides by 2, is the inequality true?)
8 < 12
8(2) < 12(2)
16 < 24
YES!
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Do You Really Understand?
• Let’s see if this still really makes sense…
(If we multiply both sides by -2, is the inequality true?)
8 < 12
8(-2) < 12(-2)
-16 < -24THIS STATEMENTIS NOT TRUE. WENEED TO FLIP THEINEQUALITY SIGNTO MAKE THIS ATRUE STATEMENT.
-16 > -24
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Solving Inequalities
• So apparently there are a few basic rules we have to follow when solving inequalities.
• If you break these rules you will answer the question incorrectly!
• DON’T BREAK THE RULZ!
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Rule #1
• Don’t forget who the bigger number is!– Example:
9 > x
– It is okay to rewrite this statement as
x < 9
– If 9 is bigger than “x”, that means that “x” is smaller than 9.
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Rule #2
• When multiplying or dividing by a negative number, reverse the inequality sign.– Example:
-5x > 15-5 -5
X < -3
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Solve Each Inequality & Graph
Example 1:
m + 14 < 4-14 -14
m < -10
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Solve Each Inequality & Graph
Example 2:
- 7 > y - 1
+1 +1 -6 > y
y < -6
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Solve Each Inequality & Graph
Example 3:
k < 10-3
(-3) (-3)
k > -30
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Solve Each Inequality & Graph
Example 4:
2x + 5 ≤ x + 1 -x -x
-5 -5
x < -4
x + 5 ≤ 1