Wed, 2/1 SWBAT

1
Wed, 2/1SWBAT
solve inequalities using addition, subtraction,
multiplication, division

• Agenda
• WU (5 min)
• Review HW1 (10 min)
• Inequalities charts (10 min)
• Solving inequalities 8 examples (20 min)
• Warm-Up
• 1. Take out HW1
• 2. Set up notes Topic Solving inequalities
• HW2Solving Inequalities

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Phrases for Inequalities Phrases for Inequalities Phrases for Inequalities Phrases for Inequalities
lt gt

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Phrases for Inequalities Phrases for Inequalities Phrases for Inequalities Phrases for Inequalities
lt gt
less than fewer than greater than more than at most no more than less than or equal to at least no less than greater than or equal to
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Endpoints (when graphing on a number line) Endpoints (when graphing on a number line) Endpoints (when graphing on a number line) Endpoints (when graphing on a number line)
lt gt

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Endpoints (when graphing on a number line) Endpoints (when graphing on a number line) Endpoints (when graphing on a number line) Endpoints (when graphing on a number line)
lt gt
Open Circle Open Circle Closed circle Closed circle
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Interval Notation Interval Notation Interval Notation Interval Notation
lt gt
( ) ( )
Examples x gt 4 (4, 8 ) -2 x 5 -2,
5 -2 lt x 5 (-2, 5
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Interval Notation Interval Notation Interval Notation Interval Notation
lt gt
( ) ( )
Examples x 4 or x lt 1 (-8, 1) 4,
8) Always use parenthesis with Infinity
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1st, Tues,
2/7SWBAT solve inequalities using addition,
subtraction, multiplication, division

• Agenda
• WU (10 min)
• Review HW1 Absolute value inequalities (10 min)
• Solving inequalities 8 examples (25 min)
• Warm-Up
• Solve for n 3.7 n 10.6 3.2
• Solve for x 7.25 x 1 6.8 21.3
• HW2Solving Multi-Step Inequalities

9

• Solving and Graphing Inequalities by Addition
  and Subtraction

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Directions Solve the inequality, graph the
solution on a number line.

• Ex 1 d 14 -19
• Ex 2 22 gt m 8
• Ex 3 Three added to a number is no more than
  twice the number.

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WARNING!!!!! (Example 2 3)

• An equation such as x 5 can be written as 5 x
• (because of the Symmetric Property of Equality)
• You CANNOT rewrite an inequality such as 3 lt x as
  x lt 3
• The inequality sign always points to the lesser
  value (or its eating the bigger number.)
• In 3 lt x, the inequality points to 3, so to write
  the expression with x on the left, use x gt 3

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• Solving and Graphing Inequalities by
  Multiplication and Division

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Very important.

• When you multiply or divide each side of an
  inequality by a negative number you always
  reverse or flip the inequality sign.
• lt ? gt
• gt? lt
• ?
• ?

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RATIONALE

• 7 gt 4
• 7(-2) gt 4(-2)
• -14 gt -8

NOT TRUE! You must change the inequality
symbol -14 lt -8
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Directions Solve the inequality, graph the
solution on a number line.

• Ex 1 -7d 147
• Ex 2 5n -25
• Ex 3
• Ex 4
• Ex 5

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• Solving and Graphing Multi-Step Inequalities

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• Tues, 2/7
• SWBAT solve multi-step inequalities
• Agenda
• Five WU problems below (15 min)
• Double math courses (5 min)
• Review HW2 multi-step inequalities (10 min)
• Review Quiz (5 min)
• Electras truck problem (10 min)
• WU Solve each inequality write in interval
  notation
• 6(x 11) 4x -72
• Two times the difference of a number and five is
  no more than eight.
• -7(k 4) 11k 8k 2(2k 1)
• 2(4r 3) 22 8(r 2)

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Geometry AND Honors Advanced Algebra with
Trigonometry (Algebra II)

• Infinity Math Sequence for students that take
  Geometry and Honors Advanced Algebra in 10th
  grade

9th 10th 11th 12th
Honors or Regular Algebra Honors or Regular Geometry and Honors Advanced Algebra Honors Pre-Calculus AP Statistics (college credit 4) (optional) AP Calculus (college credit 4) AP Statistics (college credit 4) (optional)
19

• Electra needs to rent a truck for a day to move
  some furniture. The table below shows the rates
  of the two truck-rental companies near her home.
• a.) Write an inequality that Electra can use to
  find the maximum number of miles that she can
  drive and spend less with Company A than Company
  B. Be sure to identify your variable or
  variables.
• b) Find the maximum number of miles that
  Electra can drive so that she spends less than
  she would for a truck rented from Company B.

Company Daily rate Per mile charge
A 29.95 0.87
B 72.00 0.00
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Thurs, 2/9SWBAT
solve compound inequalities

• Agenda
• WU (5 min)
• Solving compound inequalities 6 examples (25
  min)
• Two open ended compound inequalities (10 min)
• Work on HW2 or HW3 (10 min)
• Warm-Up
• -(3t 5) 7 gt 8t 3
• HW3Solving Compound Inequalities

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• Solving and Graphing Compound Inequalities

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• Inequalities Containing and
• To ride a roller coaster, you must be at least 52
  inches tall, and your height cannot exceed 72
  inches.
• If h represents the height of the rider, we can
  write two inequalities to represent this.
• At least 52 inches Cannot exceed 72 inches
• h 52 and h 72
• The inequalities h 52 and h 72 can be
  combined and written without using and as 52
  h 72
• Graph the inequality sandwich

Variable is isolated
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You try!
Inequalities Containing and

• Solve and graph the compound inequality. Write
  it two different ways.
• 1.) -2 lt x 3 lt 4
• 2.) -5 lt 3p 7 22

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• Inequalities Containing or
• SNAKES Most snakes live where the temperature
  ranges from 750 F to 900 F. Write an inequality
  to represent temperatures where snakes will not
  thrive.
• Let t temperature
• t lt 75 or t gt 90
• Graph the inequality torpedo

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You try!
Inequalities Containing or

• Solve and graph the compound inequality.
• 5n 1 lt -16 or -3n 1 lt 8
• The product of -5 and a number is greater than 35
  or less than 10.

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• OPEN ENDED 1 Write a compound inequality
  containing and for which the graph is the empty
  set.
• Sample answer x -4 and x 1
• OPEN ENDED 2 Create an example of a compound
  inequality containing or that has infinitely many
  solutions.
• Sample answer x 5 or x 1

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Tues, 2/SWBAT solve compound
inequalities

• Agenda
• WU (10 min)
• Review HW3 and HW4 (20 min)
• Solve the inequality
• 1.) Solve for a 12 (a 3) gt 4a (a 1)
• HW4 Solving Compound Inequalities Chemistry
  Geometry

28

• Chemistry The acidity of the water in a swimming
  pool is considered normal if the average of three
  pH readings is between 7.2 and 7.8. The first
  two readings for the swimming pool are 7.4 and
  7.9. What possible values for the third reading
  p will make the average pH normal?

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The value for the third reading must be between
6.3 and 8.1, inclusive.
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• GEOMETRY The Triangle Inequality Theorem states
  that the sum of the measures of any two sides of
  a triangle is greater than the measure of the
  third side.
• a.) Write and solve three inequalities to express
  the relationships among the measures of the sides
  of the triangle shown above.
• b.) What are the possible lengths for the third
  side of the triangle?
• c.) Write a compound inequality for the possible
  values of x.