Algebraic Equation Basics

Equations

An equation says two mathematical expressions are the same. The equal sign (=) in an equation shows that the left side is equal to the right. Here's an example:

3+2 = 5

The left hand side, 3+2, is the same or equal to the right hand side, 5. It works like an old fashioned scale.

Algebraic Equations - A Balancing Act

Play this game if you want to know how a old fashioned scale works. The scale is balanced when things on the left weight the same as the things on the right. In the old days before electronic scales, people would put something on the left hand side of the scale, like a bag of apples, and they would put weights on the left. You'd know how much the apples weighed when the weights on the left caused the scale to balance.

Poddle Weigh In

Inverse Operations

Source: Math Is Fun

Inverse Operation is "The operation that reverses the effect of another operation."

Click here for a good video on Inverse Operations

Take a look at this description of how inverse operations works:

Example 1: Addition and subtraction are inverse operations.

If you have 2 candy bars and you add 8 more, then you would have 10:

2 + 8 = 10

If you started with 10 candy bars and you eat 8, you would have 2.

10 - 8 = 2

Another way to look at it - you subtract 8 from both sides of the original equation to keep it balanced.

Example 2: Multiplication and division are inverse operations.

If 4 people come to your party and they each bring 3 cookies, then you would have 12 cookies:

4 x 3 = 12

What if instead, you made 12 cookies and 4 people came to your party. They could take home 3 cookies each:

12/4 = 3

Another way to look at it - you could divide both sides of the original equation by 4 to keep it balanced.

Video Tutorials

Watch the series of Khan Academy The Why of Algebra. This series of videos will give you a solid foundation for understanding Algebraic Equations. They provide a multitude of examples. Watch as many as you need to in order to understand what is an Algebraic Equation and why and how you do things to "both" sides of an equation to solve it.

After watching the recommended Khan Academy videos series, you might like to see two other videos from Khan Academy which use a Yoga class as an example:

Online Activities

Here are some fun ways to practice your knowledge on Algebraic Equations:

There are two games on this page. Select either Solving (one step) Equations with Addition and Subtraction or Multiplication and Division.

Solve two step equations.

This interactive mathematics resource allows the user to explore and interpret word problems by evaluating expressions and solving equations in a variety of different contexts.

Solving Equations

Translating and Solving Equations

Worksheets

Use these for practice. Some of the sites allow you to print the questions. Others are online only. In either case, you should systematically work through the problems on paper and then double check to make sure your answers are correct.

Algebra.Help - Online tool with step-by-step solutions

Soft schools - Generate your own worksheets. Select from one step addition, one step subtraction, addition & subtraction, one step multiplication and two step multiplication.

Adapted Mind - Algebraic Formulas Practice Problems - evaluate real world word problems.

Math Drills - Select Solving Linear Equation Worksheets, then choose the type of problem you'd like to practice, and click on a letter to the right.

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