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 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
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 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

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# Algebraic Expression

1.3 Linear Equations

An equation is two expressions that are equal (same).
equal =>" = "

Examples

Linear equations have linear expressions.
Examples

More Algebraic Properties

Identity Property

 Examples Examples

Inverse Property

 Examples Examples

Equation Properties

If a =b then
If a =b then

Multiplication/Division property of equality

 If a =b then Note : c ≠ 0 If a =b then

Using the inverse property with the equality properties, we can solve basic equations.

Example

 or or

Example

Example

or

Example

Example

When we have multiplication and addition in a problem.
Example

 or Note:

Which seems easier?

Examples

Examples

Before moving terms, we should simplify the expressions first.
Examples

Solving
1. Simplify each side of the equation.
2. Move terms by adding or subtracting
3. Divide by the coefficient

Examples

Homework:
Solve the equations.

1.4 Eliminating Denominators
Fraction:

What is the operation for the fraction?

What is the inverse operation?

To eliminate denominators, we multiply by a common denominator.

A common denominator (C.D.) can be found by multiplying the different denominators
together.
Note: This may not be the least common denominator.

Example

Different denominators :3 and 5

multplying both sides by the C. D.

Distributing

Simplifying

Now solve the linear equation

 Example Example Example Example

Homework: