3'3 Solving Equations w Variables on Both Sides

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3.3 Solving Equations w/ Variables on Both Sides

• Goals
• How to collect variables on one side of an
  equation
• How to use algebraic models to answer questions
  about real-life situations
• Why you ask!!!
• You will need to write and solve equations w/ the
  variable on both sides for some real-life
  situations such as comparing costs (and in
  Geometry

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Collecting Variables on One Side

• 73 5x 7x 11
• 7(2 m) 3m 4
• -7a -12a 65
• Hint Collect variables on the side w/ the
  greater variable coefficient!

• The strategy for solving such equations is to
  collect like variables on the same side. Some
  people prefer to collect like variables on the
  left side, but we prefer the following guideline
  which avoids a negative coefficient.

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Collect Variables

• With Variables on Both Sides we must 1st
  eliminate/move one of the variables from one
  side. So we either add or subtract it to the
  other side.
• 2nd we follow our rules for solving an equation

• x 4 2x 6
• -x -x
• 4 x 6
• 6 6
• 10 x
• x 10

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Solving w/ Variables on Both Sides

• 7x 19 -2x 55
• 2x 2x
• 9x 19 55
• - 19 - 19
• 9x 36
• 9 9
• x 4

• 80 6y 4y
• 6y 6y
• 80 10y
• 10 10
• 8 y
• Get all the variables to one side of the equation!

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More Complicated Equations

• Use the Dist. Property
• Combine Like Terms
• Move the variables to one side of the equation
• Follow your Rules
• Add 2 to both sides
• Just Change the Signs
• Check your Answer

• 4(1 x) 3x -2(x 1)
• 4 4x 3x -2x 2
• 4 x -2x 2
• x x 2
• 4 -x 2
• 2 2
• 6 -x
• -6 x

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Try These w/ A Partner

• 2(12x 16) -3(x 2)
• 7(2 x) 5x
• A local store charges 8 to rent a video game for
  three days. You must be a member to rent from
  the store, but the membership is free. A
  video-game club in town charges only 3 to rent a
  game for three days, but the membership in the
  club is 50 a year. Which membership is more
  economical, as in how games would need to be
  rented before the cost is the same?

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Understanding the ProcessKEEP THESE IN YOUR
NOTES, BUT SHOW COACH BARNETT

• Write the steps you use to solve
• -3x 5 9x 19. Beside each step, write an
  explanation of the step. Then show how to check
  your answer.
• Which step would you do first to solve the
  equation 6y (3y 6) -14 5y? Explain your
  answer.

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Assignment

• P. 138
• 1-12
• 13-29 odd
• 37, 38, 41, 42
• 43-54 odd