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Solving Linear Equations

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					Solving Linear Equations
             Linear Equations
•   Equations like
    y=x+5
    3a + 2d – f = 7


•   When the solutions of linear equations
    are graphed, they make a line
                   The Plan
• This thrilling lesson
  focuses on solving for
  single variables with
  Addition         x + 5 = 17
  Subtraction      w–4=8
  Division         k3=4
  Multiplication   q  2 = 24
           What is a Variable?
• Simple – it’s a symbol that represents a quantity
• Variables are often letters like:
  x, y, and z




                          Any symbol can be
                          used as a variable
           What is a Variable
• In the equations:     x–5=2
                      x–4=8
                      x3=4
                      x  2 = 24

  The variable is x
      Solving for Variables
Given an equation with one variable, it is
possible to find the variable algebraically

     i.g., You can find the value of x that makes
                     “x + 4 = 8” true
             Solving for Variables

       To solve for a variable isolate it to one side of the = sign


Equation
   •    x+5=8                 X=8-5

   •    x–7=2                 X=2+7

   •    x2=3                 X=3x2

   •    x3=9                 X=9/3
                 Noticing Patterns
       Isolating a variable is easy…if you know how

       Do you notice any patterns between these equations and the
       previous?
Equation                              Isolated Variable Equation
   •     x+3=8                           x=8–3

   •     x–5=2                           x=2+5

   •     x2=8                           x=82

   •     x  3 = 12                      x = 12  3
          Addition Equations
  Equation                                      Isolated Variable
  x+5=8                                        x+5–5=8–5
  x+4=0                                        x+4–4=0–4
  x + 9 = 15                                   x + 9 – 9 = 15 – 9
  x+35                                        x+3–35–3
  x+1=8                                        x+1–1=8–1
  x+55                                        x+5–55–5

To isolate variables in addition equations, subtract the number on the
variable side from both sides of the equation
     Subtraction Equations
  Equation                                     Isolated Variable
  x–5=8                                       x–5+5=8+5
  x–4=0                                       x–4+4=0+4
  x – 9 = 15                                  x – 9 + 9 = 15 + 9
  x–35                                       x–3+35+3
  x–1=8                                       x–1+1=8+1
  x–55                                       x–5+55+5

To isolate variables in subtraction equations, add the number on the
variable side to both sides of the equation
          Division Equations
  Equation                                     Isolated Variable
  x  5 = 15                                  x  5  5 = 15  5
  x  4 = 16                                  x  4  4 = 16  4
  x9=0                                       x99=09
  x36                                       x3363
  x18                                       x1181
  x5=5                                       x55=55

To isolate variables in multiplication equations, divide the number on
the variable side from both sides of the equation
   Multiplication Equations
  Equation                                     Isolated Variable
  x5=3                                       x55=35
  x4=0                                       x44=04
  x91                                       x9919
  x3=6                                       x33=63
  x18                                       x1181
  x5=5                                       x55=55

To isolate variables in division equations, multiply the number on the
variable side to both sides of the equation
    Recognizing Patterns
Operation       Opposite

+                  –

–                  +

                  

                  

Equation                       Isolated Variable Equation
   x+3=8                            x=8–3
   x–5=2                            x=2+5
   x2=8                            x=82
   x  3 = 12                       x = 12  3
    Recognizing Patterns
Operation Opposite
                               • Use the
                                 opposite of an
+            –                   operation with
–            +                   the number to
                                 isolate the
            
                                 variable
            




Equation                 Isolated Variable Equation
    x+3=8                     x=8–3
    x–5=2                     x=2+5
    x2=8                     x=82
    x  3 = 12                x = 12  3
                 Review
• Variables are symbols used to represent a
  quantity
• To solve for variables, first isolate them
• Isolate variables by doing the opposite
  operation on them to both sides of the =
  sign
• Equations are fun!
             Additional Equations
           Addition                 Click mouse to see answers

x + 6 = 12            x = 12 – 6
x+58                 x8–5
x+2=9                 x=9–2
x+3=8                 x=8–3
x+06
                      x6–0
x+4<5
                      x<5–4
x + 5 = -2
                      x = -2 – 5
x+60
                      x0–6
x + 45 = 4 + 11       x = 15 – 45
x + 2 + 12  4 + 6
                      x  10 – 14
        Additional Equations
                                     Click mouse to see answers
         Subtraction
x–6=5                  x=5+6
x–5<8                  x<8+5
x–2=9                  x=9+2
x – 3 = 19             x = 19 + 3
x–0=7                  x=7+0
x–65                  x5+6
x – 5 = -2             x = -2 + 5
x–6=0                  x=0+6
x – 45 = 8 + 11        x = 19 + 45
x – 2 – 12 < 4 + 7     x < 11 + 14
        Additional Equations
                                     Click mouse to see answers
             Division
x  6 = 12              x = 12  6
x  5 = 10              x = 10  5
x  2 = 16              x = 16  2
x3<3                   x<33
x1=6                   x=61
x  4 = 20              x = 20  4
x  5  -3              x  -3  5
x6=0                   x=06
x  3 = 15              x = 15  3
x  2  10              x  10  2
        Additional Equations
                                        Click mouse to see answers
         Multiplication
x  6 = 12                x = 12  6
x  5  10                x  10  5
x  2  16                x  16  2
x3=3                     x=33
x1=6                     x=61
x  4 < 20                x < 20  4
x  5 = -15               x = -15  5
x6=0                     x=06
x  3 = 15                x = 15  3
x  2  10                x  10  2
THE END

				
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