An equation is a math statement which contains an "=" sign. A sentence is a reading/writing statement which contains a verb (a word showing action or existing). [For students of grammar, an equation would probably be called a Predicate Nominative.]

If the statements were turned around, they would still be true!

Equations are statements of equality. Think of a teeter-totter or seesaw

To remain equations, the seesaw must stay level. So, if something is done to one side of the seesaw, something of equal value MUST be done to the other side of the seesaw to keep it balanced.

If a change is made to only one side, the equation is changed to something different.

The examples above are arithmetic equations. Normally, arithmetic equations are not used, but careful examination shows how close they are to arithmetic problems.

The main difference between an equation and a problem is that the equation has an answer. The problem does not.

The equation seen most often is the algebraic equation. Algebra extends arithmetic to include symbols besides numbers (constants). Some reasons for this are to allow the study of solutions which have many answers; so problems can be discussed even when all the information is not yet available; and so rules and procedures for certain kinds of problems can be made without having to start all over again each time.

An algebraic equation is one which may contain letters, symbols and numbers. These things are called terms.

These three(3) equations all have an identical structure:

This means that ANY change to one side MUST BE DONE to the other side (side means side of the equal sign, therefore side of the equation). Here are some examples. Follow them carefully:

What happened?

In each example, the main goal was to end up with the term in the statement "solve for ___", on one side of the equal sign. Everything or anything else was to be on the other side of the equal sign. The key is to do the solution in such a way that the seesaw never tips.

Look at the equations again:

The indicates what needs to be LEFT on the one side of the equation. To do that means getting rid of something else...

Just taking it out would cause the seesaw to crash...

The only way to keep the equation balanced is to do the same thing to both sides.

What is to be done?

To end up with:

Find out what is in the way....

How to get rid of these? In math, that is simple! Use the opposite operation!

The opposite of +3 is -3; The opposite of +4 is -4 ; and the opposite of +b is -b.

BUT....since this is an equation -- use the opposite on BOTH sides of the equal sign to keep the equation (seesaw) level.

While these are nice pictures, they are poor math. Here is what is actually to be written:

The next step is to simplfy which means to combine all the terms which can be combined (like terms).

The correct procedure for the whole thing looks like this:

Remember -- with equations, show how the equation (seesaw) stays balanced (level). Don't just do mental math and plop down an answer.

Also remember: things cannot be moved around without a reason. Don't change sides, don't insert numbers in funny places. Here are some rules to solve equations:

1. Identify the operation and term (number) you need to move (get rid of) to leave the variable by itself on one side of the equal sign..
2. Use the tern (number) with its opposite operation on BOTH sides of the equation (equal sign).
3. Simplify and repeat if necessary (more than one operation)

Here are some examples of one and two step equations (step = operation):