Don't expect here a full-blown course on high-school algebra; it cannot be done, not in such limited space. These are just the bare bones, the basic ideas and rules of handling equations

Until the multiplication is carried out, we may represent the answer by some letter, usually *x*, and write

A mathematical relationship involving known numbers (like 25 or 40) and unknown ones (like *x*) is known as an **equation**. Often *x* is not given as cleanly as above, but is buried inside some complicated expression. To get a solution, one must replace the given equation (or equations) with others, containing the same information but cleaner in appearance. The final goal is to **isolate** the unknown, to make it stand apart ("isola" is island in Italian), to bring the equation to the above form, namely

(2*x* + 5)*/* 3 = 3

Parentheses here enclose quantities handled like a single number, and 2x means "2 times *x*". In algebra, **symbols** (or parentheses) **standing next to each other** are understood to be **multiplied**. If you stick to this rule, you will never be confused by the similarity between the letter *x* and the multiplication sign ×.

(computer programs, by the way, usually represent multiplication by *, placed a little lower than here.)

Now a second fundamental idea in algebra is:
**If you have an equation and modify both its sides in ***exactly the same way*, what you get is *also* a valid equation.

You may **add**, **subtract**, **multiply** or **divide** any number you wish; as long as it's done equally to both sides of the equality, the result is still valid. Also, the new equation still contains the same information as before. (But don't multiply both sides by 0 and get 0 = 0 ; the result **is** correct, but all your information has now vanished into thin air.)

For example, the equation given earlier:

(2*x* + 5)*/* 3 = 3

Multiply both sides by 3:

(2*x* + 5) = 9

Subtract 5 from both sides:

2*x* = 9 - 5 = 4

Divide both sides by 2:

*x* = 4*/* 2 = 2

and you have the result, *x* = 2. High school algebra contains a good deal more, but the above simple rules, plus the basic goal "isolate the unknown number," will get you a long way.

One last step is frequently skipped, but should not be. **Just to make sure** you haven't made a mistake along the way, take the **original** equation

(2*x* + 5)*/* 3 = 3
replace in it the unknown quantity *x* by the value you have derived--in this case, by the number 2--and check whether the two sides are indeed equal. If they are, you can rest assured that your answer is correct.