Somewhere along the way, you will encounter variables. This is where you begin to move from kid math to adult math. It's always cool to write out some long string of numbers and letters: it looks so much more impressive than simply numbers.

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Referred to as "Mr.Ralph" at Ruamruedee Internatioal School Bangkok, a pretigious school where he taught for many years, he prides himself in being able to identify areas on which students need improvement and in giving them the tools they need to succeed at math.

Somewhere along the way, you will encounter variables. This is where you begin to move from kid math to adult math. It's always cool to write out some long string of numbers and letters: it looks so much more impressive than simply numbers.


Okay. Before you freak out, just remember that a variable (usually written as a letter, such as x, although it really could be anything at all, such as a or a ) stands for a numerical value, and that throughout a given problem its value is only that value. So, if I say that 6 + x = 4x, the x on the left hand side of the equal sign has to be the same value as the x on the right hand side. Otherwise, things would be very confusing! x might have a different value in the next problem, and x doesn't have to equal other variables, like y, although it can.


In the example above, you can easily see that x equals 2, since 6 + 2 = 4 X 2. 8 = 8, right? Usually, in a problem such as this, your only goal is to "solve for x." In other words, figure out the value of (the variable) x. You write down x = 2, your teacher is happy and you're happy.


Before we go any further, though, you MUST be absolutely sure of the distinction between expressions and equations. Usually before getting to equations you will have dealt with expressions. "What's the difference?" you might ask.


Well, think of an expression in ordinary English: "I like ice cream," or "Book." A mathematical expression is much like that: it doesn't say two things have the same value. It simply makes a statement. 3y - 4, or 6X2 are expressions, AND THERE IS NO WAY FOR YOU TO DETERMINE THE VALUE OF THE VARIABLE IN AN EXPRESSION (although you may be given its value and asked to simplify it).


Conversely, an equation says that two things are equal in value: "Five dimes equal two quarters," or "Going straight for two blocks, turning right and going another block is the 'same thing' as turning right and walking a block, then turning left and going two more blocks." 3x -1 = 2x + 4 says that the two quantities are the same, AND YOUR EXPLICIT TASK IS TO FIND THE VALUE OF THE VARIABLE.


Equations are easy, though: all you have to keep in mind is that they are like a balance scale. "This equals that." Keep manipulating, and as long as you maintain the balance you'll be alright. In our example, 3x - 1 = 2x + 4. If I take 2x away from each side- the balance will still be the same, right????- I then have x - 1 = 4. Since I want to know what x is, I add 1 to each side and get x = 5. The important thing is to make sure you are always doing the same thing to both entire sides of the equation. Again, your teacher is happy and so are you!


Equations get harder very quickly. But if you understand the basic premise in solving them, you should not undergo any suffering.

Any math problem? Ralph will be happy to help you find your way. Please use the box provided to put in your math questions. We will make sure that you will receive your answers quickly. This service is free of charge and operates on a first come first serve basis.

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Math Tutorial links

• Introduction
• Finding your own way
• Knowing The Words Pre-Algebra, Algebra
• Variables and Equations - Pre-algebra, Algebra
• Postulate , aka Axiom, what is it? - Geometry
• Math Made Easy The Number Man Ralph Schatzki

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