Solving Algebraic Equations

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Solving Algebraic Equations

• Using Alge-Tiles and the balance method

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Algebraic Equations

• When solving algebraic equations we can use
  Alge-Tiles and the scale balance method
• Remember, to balance something on a scale both
  sides must weigh the same and be equal
• Alge-Tiles
• Represents an unknown or x
• Represents an unknown or -x
• Represents a single 1
• Represents a single -1

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Step No. 1

• Lets start with an example question
• How about x 2 6
• Step 1 is to show our equation with Alge-Tiles
• x 2 6

This equation is balanced
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Step 2

• We want to have only variables on the left and
  real numbers on the right
• To do that we need to remove anything that is on
  the wrong side
• We can do that by adding the opposite to the
  thing we do not want
• Hmmm . you say . best to show you what that
  means

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• x 2 6 What is the opposite of
  2, well -2 of course so lets put it on the
  left We are adding the opposite
• But are we balanced. We need to do the same
  thing to the right side, so lets add -2 to the
  right side now

Whats on the wrong side here?
The 2 on the left
OK! We are balanced now
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Step 3

• Lets cancel out stuff now
• We are left with . x 4

WE ARE FINISHED
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Another Example

• 2x 3 -7
• We are left with
• 2x -10
• Hmmm .. What now?
• Think!!
• What multiplied by 2 is -10 or can we put -10
  into 2 groups
• Hmmm well -5 is in each group so
• x -5

NOW Balance
Step 1 Alge-Tiles
Step 3 Cancel
Step 2 Add the opposites
Excellent! Another equation solved.
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Practice

• Now its your turn to try some problems on your
  own using Alge-Tiles and the Balance method
• Good Luck