Our Lesson

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Our Lesson
Inequalities with Add and Subtract
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Warm Up

1. Seven roses less than Kiran
   y 7
2. Half as many Oranges as last year ½
   m
3. One more than a number is 845 b
   1 845
4. Eleven fewer hours than her sister s
   -11
5. One-third the population of California p/3

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Lets review what we have learned in the last
lesson
Translate verbal phrases in to algebraic
expressions
Example
He weighs 180 pounds, which is 22 pounds
180 2z-22 less than double her
weight Five more hits than the Martins
h 5 Three more
than 8 times as many trees is 75 trees 8t
3 75
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Words used to express Addition/Subtraction
Addition
Subtraction
Minus Difference Less than Less Decreased by
Plus Sum More than Increased by Total
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Words used to express Multiplication/Division
Multiplication
Division
Times Product Multiplied Of Twice Thrice
Divided Quotient
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USING A VERBAL MODEL
In Mathematics there is a difference between a
phrase and a sentence. Phrases translate into
expressions sentences translate into equations
or inequalities
Expressions
Phrases
Equations or Inequalities
Sentences
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USING A VERBAL MODEL
Phrase
Expression
Phrase
6 x 12
The sum of six and a number is twelve.
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Lets get Started
Inequalities are used in many things like
nutrition, budgeting, Personal financing, and
academics.
Grams of fat in snacks
Total Grams
Grams of fat remaining
15842 g lt 68
That is, 29 g lt 68
The symbol lt indicates less than or equal to. It
is used in this situation because the total
number of grams of fat in daily diet should be no
greater than 68. If this were an equation, we
would subtract 29 from each side.
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Defining Inequality

• An inequality is a statement with a symbol of
  lt , , gt or between numerical or variable
  expressions.
• Example x 7 11. x is a variable.
• x is a very common variable that is used in
  algebra, but you can use any letter (a, b, c, d,
  ....) to be a variable

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Inequality Symbols
SYMBOL MEANING
lt     less than
gt    greater than
      less than or equal to
      greater than or equal to
 
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Procedures that leave the inequality symbol
unchanged

• Simplify both sides of the inequality by
  combining like terms and eliminating
  parenthesis
• Add or subtract the same expression on both
  sides of the inequality
• Multiply or divide both sides of the inequality
  by the same positive expression

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Rules to Solve Linear
Inequalities

• Rule No 1 - Addition
• If a lt b, then a c lt b c
• 2 lt 5
• and c 5
• a c lt b c
• 2 5 lt 5 5
• 7 lt 10
  

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ADDING SUBTRACTING INEQUALITY

• Steps-
• To solve the inequality means isolate a variable
  x
• and move the numbers to the other side of the
• inequality.
• To move the number perform the reverse
• operation.
• Addition is the reverse of
  Subtraction
• Subtraction is the reverse of
  Addition

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Solve the inequality x 7 lt 8

• Step1 Add 7 on both sides
• x 7 7 lt 8 7
• Step2 Add the numbers
• x lt 15

Inverse of -7 is 7
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Rules to Solve Linear Inequalities

• Rule No 2 - Subtraction
• If a lt b, then a - c lt b - c
• 4 lt 7
• c 2
• a - c lt b - c
• 4 2 lt 7 - 2
• 2 lt 5
  

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Solve the inequality y 6 gt -11

• Step1 Subtract 6 on both sides
• y 6 6 gt -11 6
• Step2 Simplify the inequality
• y gt -17

Inverse of 6 is - 6
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Word problems in Inequalities
To solve the word problem translate the phrases
and solve it
Phrases Translation
is at least
is at most
cannot exceed
must exceed gt
is between lt and lt
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Example
Sample Sentences
Equivalent Form
Bill is at least 21 years old
Bill age is ? 21
At most 5 students dropped the course
Students 5
The film was between 90 and 100 minutes long.
90 lt t lt 100
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Your Turn

• t - 7 lt 14 t lt 21
• 2) r 5 gt 27 r gt 32
• 3) k - 34 10 k 44
• 4) v 22 -11 v 11
• 5) y - 3 lt -8 y lt 11

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Your Turn

• 6) x 5 lt 14
  x lt 9
• 7) z 9 gt -7
  z gt -16
• 8)
• 9) c 19 -13
  c -32
• 10) u 13 25
  u 12

Boston is more than 200 miles away D gt 200
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Refreshment Time
Break Time
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LETS PLAY A GAME
Click Here to Play
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1) Lucy earned 400 and 550 in interest, the
last 2 years. How much interest must she earn
this year so that her average earnings over the
three year period is more than 600?
Let x be the amount she needs to earn. So the
average earnings would be 400 550 x

3 The average must be more than 600. So
we need to solve the inequality   600 lt 400
550 x
3 Solve the inequality by multiplying both sides
by 3, to clear the fraction, and we have 1800 lt
400 550 x Solving for x we have 850 lt x Lucy
needs to make more than 850 this year.
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2) Chris has scored a 85 and a 89 on her first
two math 23 tests.  What must she get on her
third test to have at least a total score of 270. 
n 3rd test score (89 85
n ) ? 270 n 96
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3) Kim decides to take up golf.  Her golf club
membership will cost 450 for the season she
spends 300 on the gear and now she wants to buy
golf shoes. Kim has decided not to spend more
than 1000 on golf for the season. How much at
most can she pay for the shoes.
a) Let x cost of shoes 450 300 x ?
1000 x ? 1000 750 x ? 250
Kim can at most spend 250 for the
shoes  
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Lets review what we have Learnt today

• An inequality is a statement with a symbol of lt ,
  , gt or between numerical or variable
  expressions.
• Example x 7 11. x is a variable.
• x is a very common variable that is used in
  algebra, but you can use any letter (a, b, c, d,
  ....) to be a variable

Defining Inequality
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Inequality Symbols
SYMBOL MEANING
lt     less than
gt    greater than
      less than or equal to
      greater than or equal to
 
28
ADDING SUBTRACTING INEQUALITY

• Steps-
• To solve the inequality means isolate a variable
  x
• and move the numbers to the other side of the
• inequality.
• To move the number perform the reverse
• operation.
• Addition is the reverse of
  Subtraction
• Subtraction is the reverse of
  Addition

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Word problems in Inequalities
To solve the word problem translate the phrases
and solve it
Phrases Translation
is at least
is at most
cannot exceed
must exceed gt
is between lt and lt
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You did great in your lesson today !
Be sure to practice and keep up the good work