3-5 Solving Equations with the variable on each side

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3-5 Solving Equations with the variable on each
side

• Objective Students will solve equations with the
  variable on each side and equations with grouping
  symbols.
• S. Calahan
• 2008

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Variables on each side

• When solving equations with variables on both
  sides use the Addition or Subtraction Property of
  Equality to write an equation with the variable
  on only one side.
• Example 2x 4 x 2
• 2x 4 x x 2 x
  subtract x from each side
• x 4 -2

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-2 10p 8p 1

• -2 10p 8p 1
• - 8p - 8p subtract 8p from each side
• -2 2p -1
• 2 2 add 2 to each side
• 2p 1 divide both sides by 2
• 2 2 so, p 0.5

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Solve an Equation with Grouping Symbols

• To solve equations that contain grouping symbols
  use the Distributive Property to remove the
  grouping symbols.
• Example 2(x 4) 10
• 2x 8 10

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7(m 3) 7

• 7(m 3) 7
• 7m 21 7 distribute the 7
• 21 21 add 21 to each side
• 7m 28
• 7 7 divide each side by 7
• m 4

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No solution

• Some equations with the variable on both sides
  may not have a solution.
• Example 2x 5 2x 3
• -2x -2x
• -5 3

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2m 5 5(m 7) 3m

• 2m 5 5m 35 3m
• 2m 5 2m 35 combine like terms
• -2m -2m
• 5 -35
• 5 does not equal -35 therefore this has no
  solution

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An Identity

• 3(r 1) 5 3r 2
• 3r 3 5 3r 2 distributive property
• 3r 2 3r 2 reflexive property of
  equality
• Therefore, the solution contains all real numbers

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Steps for solving equations

1. Use the Distributive Property
2. Simplify the expression on each side.
3. Use the Addition and/or Subtraction Properties of
   Equality to get the variables on one side and the
   numbers without variables on the other side.

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4. Simplify the expressions on each side of the
equals sign. 5. use

• 4. Simplify the expressions on each side of the
  equals sign.
• 5. Use the Multiplication or Division Property of
  Equality to solve.