# Section 10.3 by lFbWyi

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```									        Section 2.1

Linear Equations in One Variable
Equation

Equation- a mathematical expression
that states that two (2) quantities are
equal

** Use the equal sign (=) **

ex.   2 + 8 = 10   ex.   10 – 5 = 5
Type of Equation
Linear Equation in one variable- equation
that can be written in the form . . .
ax + b = c or ax = b
where a, b, c are constants and a   0
ex. 3x + 9 = 0         ex. 7x + 5 = 2x – 9

ex. 4(x – 2)= 6              ex. x = 6
Linear Equation = First degree equation

** First degree because the highest
power on the variable is one. **
Solution to a Linear Equation
Solution- the value that can be
substituted for the unknown variable so
the resulting statement is true

Solution Set- the set of all solutions

Used to show solution set    
To determine if a value is a
solution?
1. Substitute the value in for the unknown
variable.

2. Simplify both sides of the equation.

3. Does it make a true statement (both
sides of the equation are equal)?
• If yes, then the value is a solution.
• If no, then the value is not a
solution.
For example . . .
ex. 4 is a solution to 3x – 5 = 7 ex. 2 is not a solution to 5x – 9 = 6
3x – 5 = 7                          5x – 9 = 6
3(4) – 5 = 7                        5(2) – 9 = 6
12 – 5 = 7                          10 – 9 = 6
7 = 7                                 1  6
True Statement                     False Statement
Determine if the numbers are
solutions to the following
equations.
ex.   ½ ; 2y + 5 = 4   ex. 3 ; 4x + 3 = 18 – x
How to Solve Linear Equations
• Isolate the variable on one side of the
equation so that the number that is the
solution is on the other side.

Typically

variable          left-hand side
solution          right-hand side

**But it does not matter which side is which **
Think of = sign as a scale that
keeps everything balanced

* What you do to one side you must do to the
other in order to keep the equation balanced *
To isolate the variable use
Inverse Operations

Inverse Operations- Operations that
undo each other.

inverse operations.

• Multiplication and Division are
inverse operations.
Steps To Solve Linear Equations
1. Simplify both sides of the equation as much as possible
•   Clear Fractions
•   Combine like terms
•   Use distributive property
– 3(x + 5)
2. Move all variable terms to one side of the equation and
all constant terms to the other side of the equation
•   Variables-left side of equation, Constants-right side of
equation
•   Use addition or subtraction (Do opposite of what is given)
3. Isolate variable (make the coefficient 1) on one side of
equation and solution on the other side
•   Use multiplication or division (Do opposite of what is given)
4. Check that your solution is correct by substituting it
back into original equation to see if it makes a true
statement (both sides equal the same value)
How to remember rules!
S    A    S    M    D
I    D    U    U     I
M    D    B    L     V
P         T    T     I
L         R    I     D
I         A    P     E
F         C    L
Y         T    Y

```
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