What's an Equation?

Quick Answer:

An equation is a way of saying two things are equal; it is literally a mathematical statement of equality, hence the name "equation." Just remembering that simple fact may help you understand some of the operations performed on equations later.

Example: \(2x=8\) (two times the variable x is equal to the number 8)

One thing to remember about equations is that you can perform operations on each side of the equals sign, so long as you do the same operation to each side. Imagine that the equation represents a scale, balanced with the same weight on each side. You can add weight to either side, or remove it, so long as you do the same to each side. You can also multiply each side by the same factor, or divide. As long as you haven't changed the balance of the two expressions on either side, you still have a valid equation.

Example: Take the equation \(4x=8\). You can divide each side by 4 to get this new equation:

$$ \frac{4x}{4}=\frac{8}{4} $$ $$ x=2 $$

You've solved the equation for \(x\) by simply dividing each side by the same amount, leaving behind a very simple, and valid, equation.