What is the difference between simplifying an expression, and solving an equation?

This really gets down to the difference between an expression and an equation.

An expression is something without an equal sign. For example:

2x² + 4x + 2

Here you could simplify this by factoring:

2(x² + 2x + 1)

2(x + 1)(x + 1)

2(x + 1)²

An *equation* has an equal sign. Thus you can go a step farther and actually solve for the unknown variable.

If we had the same expression, but equal to 0, the equation would be:

2x² + 4x + 2 = 0

Again we could factor and get:

2(x + 1)² = 0

But then you would solve for x:

x + 1 = 0

x = -1

So basically, you often use the same steps to simplify both and expression and an equation, but you can only solve for the variable when the expression is equal to something. You can't "solve" an expression, you only simplify. In an equation, you probably use some simplifying to finally get the variable alone to know the solution.

Simplifying an equation is usually making the numbers or what is given to solve easier to use with, and solving an equation is using the simplifications (usually) to get the answer...

when you simplify something, you just make the problem as simple as possible... there are no need to solve for any varibles...

when you solve for something, you have to set the varible equal to the rest of the equation and solve for that varible.