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# The Basics of Algebra Study Guide

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Updated on Aug 24, 2011

Find practice problems and solutions for these concepts at The Basics of Algebra Practice Problems.

### What's Around The Bend

• Variables
• Expressions
• Coefficients
• Like Terms
• Simplifying Expressions
• The Commutative Property
• The Associative Property
• The Identity Element
• Multiplicative Inverse
• The Distributive Property

Just when you were getting used to numbers, algebra attacks. You were hip to decimals, multiplication, even fractions. But algebra is a different kind of animal. It contains letters! Yes, letters. And that's not the only thing that makes algebra stand out.

You may be asking why you need to study algebra. Well, all the math that is needed in science and engineering relies on algebra as its basic language. Do you like toasters and TVs? Do you like airplanes and air conditioning? Do you like all the smart, edgy stuff that technology makes available? It all depends on algebra.

### Letters in Math Class?

Variables are letters that are used to represent numbers. Once you realize that these variables are just numbers in disguise, you'll understand that they must obey all the rules of mathematics, just like the numbers that aren't disguised. This can help you figure out what number the variable at hand stands for.

#### Fuel for Thought

An expression is like a series of words without a verb. Take, for example, 3x + 5 or a – 3. A verb, which would be an equality or inequality symbol, would give value to the statement, turning it into an equation or inequality. These symbols include =, ≠, >, <, ≥, and ≤.

Look at this equation:

a + 4 = 7

In the equation a + 4 = 7, the letter a represents a little box. Think of the letter a as the label on the box. Inside the box is a number. Your job is to figure out what that number is. What number can you put in the box to turn the equation a + 4 = 7 into a true statement?

Let's just stick 20 into the a box. The equation becomes 20 + 4 = 7, or 24 = 7. Okay, this equation is not a true statement because 24 does not equal 7. So, a is not the number 20.

If you put 3 into the box, the equation becomes this true statement: 3 + 4 = 7, or 7 = 7.

#### Fuel for Thought

When a number is placed next to a variable, indicating multiplication, the number is said to be the coefficient of the variable. For example,

8c      8 is the coefficient of the variable c.

6ab   6 is the coefficient of both variables, a and b.

If two or more terms have exactly the same variable(s), they are said to be like terms.

7x + 3x = 10x

The process of grouping like terms together and performing their mathematical operations is called combining like terms. It is important to combine like terms carefully, making sure that the variables are exactly the same.

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