Puzzler

1
Puzzler

• Eva weighs 2.5 times as much as her sister, but
  if their 10 lb. cat sits on Evas side of the
  seesaw and their 70 lb. Dog sits on her sisters
  side, they exactly balance. How much does Eva
  weigh?

2
1.3 Solving Linear Equations

• Goals
• 1- Solve Linear Equations
• 2- Use linear equations to solve real-life
  problems.

3
Solving a Linear Equation

• Equation statement in which 2 expressions are
  equal
• Linear Equation axb where a and b are constants
  and a 0

4
Solving a Linear Equation

• A number is a Solution if the statement is true
  when the number is substituted for the variable.
• Two equations are Equivalent Equations if have
  the same solution.

5
Transformations that Produce Equivalent Equations

• If a b
• Addition Property of Equality
• Add the same number to both sides. acbc
• Subtraction Property of Equality
• Subtract the same number from both sides.
  a-cb-c
• Multiplication Property of Equality
• Multiply both sides by the same nonzero number.
  acbc
• Division Property of Equality
• Divide both sides by the same nonzero number.
  acbc

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Solving an Equation with a Variable on One Side

• (3/7)x 9 15

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Solving an Equation with Variables on Both Sides

• 5n 11 7n 9

8
Using the Distributive Property

• 4(3x-5) -2(-x8) 6x

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Solving an Equation with Fractions

• (1/3)x (1/4) x (1/6)

10
Writing and Using a Linear Equation

• A real estate brokers base salary is 18,000.
  She earns a 4 commission on total sales. How
  much must she sell to earn 55,000 total?

Total Income 55,000 Base Salary
18,000 Commission Rate 0.04 Total Sales x
11
Writing and Using Geometric Formula

• You make a 1 foot wide boundary in a rectangular
  shape around your flower garden with border
  tiles. You have enough tiles so that the outside
  perimeter of the tiles can be 38 feet. If the
  original garden is 4 feet by 8 feet, by what
  percent of its original size can you expand the
  garden to fit the border?

Perimeter 2L 2W 38 L 24x W 28x So, 38
2(24x)2(28x)
8 ft.
1 ft
4 ft.
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Now Solve

• 38 2(24x)2(28x)

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Real-Life Problem

• One phone company charges 6 cents per minute with
  a 10 monthly fee another charges 7 cents per
  minute with a 5 monthly fee. For what number of
  minutes are the costs equal? Which plan is better?

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Homework

• Pg. 22-24
• 30-36 even, 41,45-47,49