Introduction to Algebra

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Introduction to Algebra Powered By Docstoc
					ONE STEP
EQUATIONS
        ONE STEP EQUATIONS

An equation is like a balance scale
because it shows that two
quantities are equal.




What you do to one side of the
equation must also be done to the
other side to keep it balanced.
       ONE STEP EQUATIONS

  To solve one step equations, you need
     to ask three questions about the
                 equation:
• What is the variable?

• What operation is performed on the variable?
• What is the inverse operation?
   (The one that will undo what is being
        done to the variable)
   ONE STEP EQUATIONS

Example 1 Solve x + 4 = 12
What is the variable? The variable is x.
What operation is being performed on the variable? Addition.
What is the inverse operation (the one that will undo what is
being done to the variable)?                           Subtraction.
 Using the subtraction property of equality, subtract 4 from both
 sides of the equation.
The subtraction property of equality tells us to subtract
the same thing on both sides to keep the equation equal.
                        x + 4 = 12
                          -4     -4
                           x = 8
        ONE STEP EQUATIONS

    Example 2 Solve y - 7 = -13
  What is the variable? The variable is y.
  What operation is being performed on the variable? Subtraction.
  What is the inverse operation (the one that will undo what is being
  done to the variable)?                                    Addition.
   Using the addition property of equality, add 7 to both sides of
   the equation.

The addition property of equality tells us to add the same
thing on both sides to keep the equation equal.

                          y - 7 = -13
                            +7 +7
                              y = -6
      ONE STEP EQUATIONS

Example 3 Solve –6a = 12
What is the variable? The variable is a.
What operation is being performed on the variable? Multiplication.
What is the inverse operation (the one that will undo what is being done
to the variable)?                                              Division
 Using the division property of equality, divide both sides of the
 equation by –6.
The division property of equality tells us to divide the same
thing on both sides to keep the equation equal.
                       –6a = 12
                       -6    -6
                         a = -2
      ONE STEP EQUATIONS
Example 4 Solve b = -10
What is the variable?
                      2 The variable is b.
 What operation is being performed on the variable? Division.
 What is the inverse operation (the one that will undo what is
 being done to the variable)?                         Multiplication
 Using the multiplication property of equality, multiply both sides
 of the equation by 2.
The multiplication property of equality tells us to multiply
the same thing on both sides to keep the equation equal.
                       b
                         = -10
                       2
                      b
                  2 •    = -10 • 2
                      2
                       b = -20
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
     Answers:

1.   r = 13
2.   g = 4
3.   p = - 22
4.   b = - 17
5.   v = 13
6.   w=-6
       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. Read/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?
      Try it !

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.

				
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