Solving Linear Equations

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Solving Linear Equations

• Multi-Step Equations

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Solving Multi-Step Equations

• To find the solution to an equation we must
  isolate the variable.
• We isolate the variable by performing operations
  that will eliminate (cancel) the other numbers
  from the expression.

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Solving Multi-Step Equations

• We have seen how to eliminate a constant
  (Addition Property of Equality) how to
  eliminate a coefficient (Multiplication Property
  of Equality). What if an equation has both a
  constant and a coefficient to be eliminated?
• This is called a Multi-Step Equation.

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Solving Multi-Step Equations

• This is a multi-step equation. 3x 5 17
• We must eliminate the constant, 5, and the
  coefficient, 3, to isolate the variable, x.
• The order that we use the equality properties is
  very important, we must follow the order of
  operations in reverse!

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Solving Multi-Step Equations

• In the expression 3x 5, the order of operations
  tells us to multiply 3 times x, and then add the
  product to 5. Eliminating in reverse order, we
  need to eliminate the 5 first by adding (-5)

3x 5 (-5) 17 (-5)
3x 0 12
3x 12.
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Solving Multi-Step Equations

• Now we need to eliminate the 3 by multiplying 1/3

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Solving Multi-Step Equations

• Check the solution

3x 5 17
3(4) 5 17
12 5 17
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Solving Multi-Step Equations

• The Steps
• If the variable is on the right side of the
  equation, swap sides.
• If there is a constant on the variable side, add
  the opposite of the constant to both sides of the
  equation.
• If there is a coefficient in front of the
  variable, multiply both sides of the equation by
  the reciprocal of the coefficient.

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Examples
Check 3k - 4 8 3(4) - 4 8
12 - 4 8 8 8 v
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Examples
Check 5x 1 -14 5(-3) 1 -14
-15 1 -14 -14 -14 v
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Examples
Check -2x 1 1 -2(0) 1 1
0 1 1 1 1 v
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Try These!
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Solutions!
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Solutions!
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Solutions!