Linear Equations and Literal Equations

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Linear Equations and Literal Equations
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Equality and Balances
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• Will this balance? If not, which way will it tilt?

• How could we make it balance?

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Exercise Draw a picture of what the following
would look like on balance scales.

• 2 ( 3 x 5 ) 7 ( 2 x 5 ) 1
• 3 ( 2 x 4 ) 1 ( 2 x 6 ) 2
• ( 10 / 2 ) ( 3 x 2 ) ( 8 / 2 ) x ( 6 / 3)
  

• http//illuminations.nctm.org/ActivityDetail.aspx?
  id26

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Find the possible missing values to balance the
equations
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A linear equation in one variable is an equation
that can be written in the form
ax b 0
where a and b are
real numbers and a is not zero.

• Examples
• 4x 2 0
• 4x 4
• 2x 3x - 1

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• We solve linear equations in x by transforming
  the equation to an equivalent equation of the
  form
• x d
• where d is a real number.
• (That is we get x by itself on one side.)
• The solution set is d .
• example x 2 4 is equivalent to x 6

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Properties of Equality

• Let A, B, and C be real numbers.
• If A B is a true statement, then the following
  are also true
• A C B C
• A C B C
• AC BC
• A/C B/C (unless C 0)

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• Solving equations on a balance scale applet
• http//nlvm.usu.edu/en/nav/frames_asid_324_g_3_t_2
  .html?openinstructions

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Solving Equations with Two Color Chips and Cups

• Activity Packet p. 169

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Solving Equations with Two-Color Counters and
Pattern Blocks

• Activity Packet p. 173

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Solving Equations involving fractions with
two-color counters and pattern blocks.

• Activity packet p. 175

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• A literal equation is an equation with two or
  more unknowns.
• A formula is an equation that models a known
  relationship between two or more quantities.
• Examples
• Solve A ½ bh for h.
• Solve A P Prt for P. P.
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