## What is an Algebra?

**Algebra** is a problem-solving language that is used to solve real-life problems. It has four basic components, which tend to next within each other.

Translating verbal phrases into algebraic expressions enables you to solve real-life problems.

1. Symbolic representations and applications of the rules of arithmetic.

2 . Rewriting (reducing, simplifying, factoring) algebraic expressions into equivalent forms.

3. Creating and solving equations.

4. Studying relationships among variables by the use of functions and graphs.

Notice that one of the components deals with expressions and another deals with equations. As you study algebra, it is important to understand the difference between simplifying or rewriting an algebraic expression, and solving an algebraic equation. In general, remember that a mathematical expression has no equal sign, whereas a mathematical equation must have an equal sign.

When you use an equal sign to rewrite an expression, you are merely indicating the equivalence of the new expression and the previous one.

Original expression ((a + b)c ) equals (=) Equivalent expression (ac + bc)

In previous post you studied simplifying algebraic expressions. In this post you will study ways to construct algebraic expressions from written statements by first constructing a verbal mathematical model.

Example : You accepy a part time job for $9 per hour. The job offer states that you will be expected to work between 15 and 30 hours a week. Because you don’t know how many hours you will work during a week. Your total income for a week is unknown. Moreover, your income will probably vary from week to week. By representing the variable quantity by the letter x, you can represent the weekly income by the following algebraic expression

pay par hour . number of hours = 9 dollar . x hours = 9x

Note the hidden operation of multiplication in this expression. Nowhere in the verbal problem does it say you are to multiply 9 times x. It is implied in the problem. This is often the case when algebra is used to solve real-life problems.

A good way to learn algebra is to do it forward and backward. Keep in mind that other key words could be used to describe the operation in each expression. Your goal is to use key words or phrases that keep the verbal description clear and concise.

Translating algebraic expressions into verbal phrases is more difficult than it may appear. It is easy to write a phrase that is ambiguous.