# 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
Addition/Subtraction property of equality**

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:**