Solving One-Step Equations

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Solving One-Step Equations
A Students Tutorial

• Stacie Courtney
• Unit 5
• Individual Project
• Nov.14, 2003

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Learning Outcomes

• Students will determine the inverse relationship
  between addition and subtraction, multiplication
  and division
• Students will use a variety of methods and
  representations to create and solve one-step
  linear equations.
• Students will be able to write and solve one-step
  equations presented in the form of word problems.

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Solving Addition and Subtraction Equations

• Key Words
• Solutions Value(s) that make the equation true.
• Inverse Operations Operations that undo each
  other.
• Equivalent Equations Equations that have the
  same solution.
• Addition Property of Equality States that for
  any numbers a, b, and c, if a b, then a b b
  c.
• Subtraction Property of Equality States that
  for any numbers a, b, and c, if a b, then a c
  b c.

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Solving Addition and Subtraction Equations

• Steps to Solving an Addition or Subtraction
  Equation
• To solve an equation you want to get the variable
  term(s) alone on one side of the equal sign.
  Isolate the variable
• To solve an equation you must use its inverse
  operation. The inverse operation of addition is
  subtraction and the inverse operation of
  subtraction is addition.
• You must also remember that whatever you do to
  one side of the equal sign you have to do to the
  other.

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Example of Addition Equation

• Example
• x 5 6 1) I need to get the x on the right
  side of the equal sign by itself. To do this
  I need to do the inverse operation of 5,
  which is 5.
• x 5 6 2) Be sure to remember your rules for
  -5 -5 adding and subtracting
  integers. (See additional flowchart if
  needed)
• x 1 3) Check equation by filling in the
  variable.
• (1) 5 6 This is a true statement, so
  we are correct.

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Example of Subtraction Equation

• Example
• -10 y 2 1) I need to get the y on the
  right side of the equal sign by itself. To
  do this I need to do the inverse operation
  of - 10, which is 10.
• -10 y 2 2) Be sure to remember your
  rules for 10 10 adding and subtracting
  integers. (See additional flowchart if
  needed)
• -y 12 3) The variable cannot be negative.
  To correct this you multiply both sides by a
  negative, which changes both signs.
• y - 12 4) Check equation by filling in the
  variable. - 10 (-12) 2 This is a true
  statement, so we are correct.

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Solving Multiplication and Division Equations

• Key Words
• Solutions Value(s) that make the equation true.
• Inverse Operations Operations that undo each
  other.
• Equivalent Equations Equations that have the
  same solution.
• Multiplication Property of Equality For any
  numbers a, b, and c, if a b, then a(c) b(c).
• Division Property of Equality For any numbers
  a, b, c, if a b, then a c b c.

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Solving Multiplication and Division Equations

• Steps to Solving a Multiplication or Division
  Equation
• To solve an equation you want to get the variable
  term(s) alone on one side of the equal sign.
  Isolate the variable
• To solve an equation you must use its inverse
  operation. The inverse operation of
  multiplication is division and the inverse
  operation of division is multiplication.
• You must also remember that whatever you do to
  one side of the equal sign you have to do to the
  other.

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Example of Multiplication Equation

• Example
• 20 -2 x 1) I need to get the x on the right
  side of the equal sign by itself. To do
  this I need to do the inverse operation
  of multiplying by 2, which is divide by 2.
• 20 -2 x 2) Be sure to remember your rules
• -2 -2 for multiplying and dividing
  integers. (See additional flowchart if
  needed)
• -10 x 3) Check equation by filling in the
  variable. 20 -2 (-10) This is a
  true statement, so we are correct.

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Example of Division Equation

• Example
• n 5 1) I need to get the n on the right side
  6 of the equal sign by itself.
  To do this I need to do the inverse operation
  of dividing by 6, which is multiplying by 6.
• (6) n 5 (6) 2) Be sure to remember your
  rules for
• 6 multiplying and dividing integers.
  (See additional flowchart if needed)
• n 30 3) Check equation by filling in the
  variable.
• 30 5 This is a true statement, so we
  6 are correct

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Modeling Word Problems by Writing Equations

• Organize your thoughts and work by following a
  simple outline.
• Define What is it that you are looking for?
• Relate Write the problem out in words.
• Write Using the relate statement, fill in what
  you know.
• Solve Solve for your variable using the steps
  from Section I and II.
• Check Go back and be sure you answered the
  question and it makes sense.

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Example Word Problem

• Example
• The average annual precipitation of Houston,
  Texas is about 5.2 times that of El Paso, Texas.
  If Houstons average annual precipitation is 46
  in., then what would the average annual
  precipitation of El Paso be?
• Define p El Pasos precipitation
• Relate Houstons precipitation is 5.2 times El
  Pasos precipitation
• Write 46 5.2 p
• Solve 46 5.2p
• 5.2 5.2
• p about 8.8 in.
• Check El Pasos precipitation is about 8.8
  inches, which is about 5 times that of
  Houstons.

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On Your Own Practice Problems

• Addition and Subtraction Equations
• 5 v 13
• -7 a 28
• y - ? ?
• -1.05 t 6.17

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On Your Own Practice Problems

• Multiplication and Division Equations
• 5p -75
• -8j 12.56
• y 7 35
• 107 -b 3

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On Your Own Practice Problems

• Word Problems
• Your bill for a car repair is 166.50. One third
  of the bill is for labor. The mechanic worked on
  your car for 1.5h. What is the hourly charge for
  labor?
• Two angles are supplementary if the sum of their
  measures is 180. Suppose angles A and B are
  supplementary angles, and the measure of angle A
  is 109. What is the measure of angle B?

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Solutions to the On Your Own Practice Problems

• Addition and Subtraction Equations
• v 8
• a 35
• y 1
• t -5.1

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Solutions to the On Your Own Practice Problems

• Multiplication and Division Equations
• p -15
• j -1.57
• y -245
• b -321

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Solutions to the On Your Own Practice Problems

• Word Problems
• 1.5x 55.5
• x 37 hours
• a 109 180
• a 71

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Assignment

• Now that you got the concept down go to One Step
  Equations Quiz and take the 10 question quiz.
• When you finish be sure to summarize how you did
  and submit it to the instructors drop box.