Section 5.1 Solving First-Degree Equations Variable terms -

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Section 5.1 Solving First-Degree Equations

• Variable terms -- each term contains a variable.
• Constant term -- it does not contain a variable.
• Each variable term is composed of a numerical
  coefficient and a variable part (the variable or
  variables and their exponents).
• Like terms of a variable expression are terms
  with the same variable part. Constant terms are
  also like terms.
• An equation expresses the equality of two
  mathematical expressions.

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• Example 8513 4y - 6 10
• x2 - 2x 1 0 b7
• First degree means that the variable has an
  exponent of 1.
• Example x 11 14 3z 5 8z
• 2(6y - 1) 34

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• A solution of an equation is a number that, when
  substituted for the variable, results in a true
  equation.
• 3 is a solution of the equation x 4 7
• because 3 4 7.
• 9 is not a solution of the equation x 4 7
• because 9 4 is not equal to 7.

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• To solve an equation means to find all solutions
  of the equation.
• The following properties of equations are often
  used to solve equations.

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• Addition Property
• If a b, then a c b c.
• Subtraction Property
• If a b, then a - c b - c.
• Multiplication Property
• If a b and c not 0, then ac bc.
• Division Property
• If a b and c is not 0, then a/cb/c.

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• In solving a first-degree equation in one
  variable, the goal is to rewrite the equation
  with the variable alone on one side of the
  equation and a constant term on the other side of
  the equation.

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EXAMPLE 1.

• Solve.
• a). y - 8 17
• b). 4x -2
• c). - 5 9 b
• d). - a - 36

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CHECK YOUR PROGRESS 1

• Solve.
• a. c 6 -13
• b. 4 -8z
• c. 22 m -9
• d. 5x 0

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• Steps for Solving a First-Degree Equation in One
  Variable
• 1. If the equation contains fractions, multiply
  each side of the equation by the least common
  multiple (LCM) of the denominators to clear the
  equation of fractions.
• 2. Use the Distributive Property to remove
  parentheses.
• 3. Combine any like terms on the right side of
  the equation and any like terms on the left side
  of the equation.
• 4. Use the Addition or Subtraction Property to
  rewrite the equation with only one variable term
  and only one constant term.
• 5. Use the Multiplication or Division Property to
  rewrite the equation with the variable alone on
  one side of the equation and a constant term on
  the other side of the equation.

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EXAMPLE 2

• Solve
• a. 5x 9 23 - 2x
• b. 8x - 3(4x - 5) -2x 6

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• EXAMPLE 3. Forensic scientists have determined
  that the equation
• H 2.9L 78.1
• can be used to approximate the height H, in
  centimeters, of an adult based on the length L,
  in centimeters, of the adult's humerus (the bone
  extending from the shoulder to the elbow).
• a. Use this formula to approximate the height of
  an adult whose humerus measures 36 centimeters.
• b. According to this formula, what is the length
  of the humerus of an adult whose height is 168
  centimeters?

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Literal Equations

• A literal equation is an equation that contains
  more than one variable.
• A formula is a literal equation that states a
  rule about measurement.