## 6.4 Outline

- Terminology
- equation
- true
- false
- open

- satisfy
- root
- solution
- solve – this is the last of four main processes in algebra

- equivalent equations
- types
- linear equations
- quadratic equations

- equation
- Linear equations
- equation properties
- addition property
- subtraction property
- multiplication property
- division property

- goal of equation solving
- symmetric property of equality
- change a repeating decimal to fractional form

- equation properties
- Quadratic equations
- zero-product rule
- quadratic formula
- using technology to solve
- chaos and fractals

## 6.4 Essential Ideas

An **equation** is a statement of equality, and there are three types of equations:

*open* (has a variable), *true*, and *false*. To **solve** an equation is find the replacement(s) for the variable(s) that make the open equation a true equation. There are two types of equations solved in this section:

**Linear equations:** *ax + b =*0, (*a *not equal to 0)

**Quadratic equations:** *ax*^{2 }*+ bx + c = *0 (*a *not equal to 0)

**To solve a linear equation, you can use one or more of the following equation properties:**

**addition property:** Adding the same number to both sides of an equation results in an equivalent equation.

**subtraction property: **Subtracting the same number from both sides of an equation results in a equivalent equation.

**multiplication property: **Multiplying both sides of a given equation by the same nonzero number results in an equivalent equation.

**division property: **Dividing both sides on a given equation by the same nonzero number results in an equivalent equation.

**To solve a quadratic equation, use the following properties, in order:**

**zero-product rule: **Obtain a zero on one side, and then factor the other side using the zero product rule.

**quadratic formula: **Write the equation in the form *ax*^{2} + *bx* + *c* = 0 (where *a *is not zero), and then use the quadratic formula.

Finally, algebraically simplify.