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Simplifying an expression means making it as simple as possible. Think of it like cleaning up your room. When you simplify, you get rid of anything you don't need and organize what you have.

In math, simplifying an expression involves combining like terms and performing arithmetic operations to make the expression more concise and easier to understand.

For example, in the exercise \(-5x - (-2x)\), simplifying means we should get rid of unnecessary symbols and make it as straightforward as possible. By handling the negative signs properly, we turn \(-(-2x)\) into \(+2x\). This clean-up process turns the expression into \(-5x + 2x\).

Now the expression is more manageable, and we can see it clearer to combine like terms and further simplify it.

Coefficients are numbers that stand in front of variables in an expression. They tell you how many of the variable you have. For instance, in \(-5x\), the coefficient is \-5\. It means you have \-5\ units of \x\.

Combining like terms involves adding or subtracting coefficients.

For instance, in the simplified expression from the exercise, \(-5x + 2x\), we need to add or subtract the coefficients \(-5\) and \(+2\). When doing so, you perform the arithmetic operation: \(-5 + 2 = -3\). This tells you that you have \(-3\) units of \x\.

So the expression becomes \(-3x\).

A variable is a symbol, commonly \x\, used to represent a value that can change. In our exercise, the like terms are both associated with the same variable \x\.

Like terms are terms that have the same variable raised to the same power. For example, \(-5x\) and \(+2x\) both have the variable \x\ to the power of 1. This is why we can combine them by adding or subtracting their coefficients.

If you encounter terms with different variables or different powers, you can't combine them in the same way.

For instance, \-5x\ and \+3y\ are not like terms, because they have different variables, so you can't combine them.