Solving one step equations by jennyyingdi

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									Solving one step equations
Rules to Remember
                 Quick Facts and
                   Definitions:

            When solving an equation,
             the goal is to get the
             variable by itself on one
             side of the equation.
            Addition and subtraction
             are inverse operations.
             (opposites)
            Multiplication and
             division are inverse
             operations. (opposites)
        Solving Equations Requires
                BALANCE!
Your equals sign will be
 the fulcrum (balancing
 point)!

Just remember, whatever
  you do to one side must
  be done to the other side
  to maintain
  balance……..
           Addition / Subtraction




   If the number to move is positive, subtract it from
    both sides of the equation.
   If the number to move is negative, add its positive
    value to both sides of the equation.
       Solving with Addition
     Solve the following equation for x:
               x – 4 =         9
                   +4         +4
                x       =     13
      We are able to get the x by itself
        by ADDING 4 to each side!
(you WILL show this step in your homework!!)
     Solving with Subtraction
     Solve the following equation for p:
               p + 7 =         21
                    -7         -7
               p        =      14
       We are able to get the p by itself
    by SUBTRACTING 7 from each side!
(you WILL show this step in your homework!!)
          Solving with Division
          Solve the following equation for m:
                     3m =       18

   Divide both sides by 3 and simplify -- your work should
    look like this   :

                    3m =       18
                     3           3
                      m =      6

       (you WILL show this step in your homework!!)
 Solving with Multiplication




 Problems involving fractions are solved using
multiplication, and the knowledge of multiplicative
                inverses (reciprocals)
                         Example :
      Solve the following equation for n:

                2n      =        3
                5                7
   Multiply each side by the inverse of 25 :

           5 • 2n          =       3 • 5
            2   5                   7   2

                 n         =     15
                                  14
Your Turn:
   Solve the following equations
      with one step (show your
      work!!):
   1. r + 4 = 17
   2. g - 15 = -11
   3. 13 + p = - 9
   4. -5b = 85
   5. - 7v = - 91
   6.   w = -2
        3        9
                 Answers:
1.   r = 13
2.   g = 4
3.   p = - 22
4.   b = - 17
5.   v = 13
6.   w = - 2/3
           Word Problems
       with One Step Equations
You will need to know how to solve word
   problems involving these equations, by using
   the four-step problem solving plan:
1. Explore the problem
2. Plan the solution
3. Solve the problem
4. Examine the solution
        1. Explore the problem
     First, read the
    problem carefully,
    then:
   Identify what
    information is
    given
   Identify what you
    are asked to find
            2. Plan the Solution
   Choose a variable to represent the unknown that you
    are trying to solve for
   Create an algebraic equation for solving
3.   Solve the Problem   4.   Examine the Solution


    use algebraic
     methods                 Is your answer
                              “reasonable” ?




    Show your work!         Did you check your
                              work to be sure?
                   Let’s try it!
Read the following:
One mile is equal to approximately 1.6 kilometers. A
  local running club is holding a 10 kilometer race.
  What is the length of the race in miles?

   Define aVariable Let m = the number of miles
   1.6 • m = 10
   Divide both sides by 1.6 (calculators ok)
   m = 6.25
   The length of the race is 6.25 miles.
                One more !
Write an Equation and Solve the Problem:
Noah received a paycheck on Friday. After buying
  some athletic shoes for $112, he had $96 left.
How much was his paycheck?
 Let p = paycheck

 p - 112      =     96
   + 112          +112
 p           =     208
 Noah’s paycheck was $208.
          Homework:
  One step equation worksheet:
You MUST show your work to get
   credit on this assignment!!!
           Properties of Equality
1.   Addition: If a = b then a + c = b + c.

2. Subtraction: If a = b then a – c = b– c.

3. Multiplication: If a = b then ac = bc.

4. Division: If a = b and c ≠ 0 then a/c = b/c

								
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