# 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
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!

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
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
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
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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