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In algebra, expressions often have terms that can be grouped together to simplify the expression. "Combining like terms" is a basic algebraic process used to simplify expressions in a more readable form.
For terms to be "like," they must:

• Contain the same variable or variables
• Have those variables raised to the same power

In the expression we are dealing with, which is \(2n - 3n\), both terms have the variable \(n\) to the same power of 1. It's important to recognize that the only thing separating these similar terms is their coefficients, not their "likeness," which is derived from their variable parts.
By identifying and combining like terms, you can reduce complexity in equations and make solving them more straightforward.

Coefficients are the numbers placed in front of the variables in algebraic expressions. They tell us how many times to multiply the variable by. In the expression \(2n - 3n\), 2 and -3 are the coefficients of \(n\).
When combining like terms, it is these coefficients that we add or subtract to simplify the expression.
For example:

• For \(2n\), the coefficient is 2
• For \(-3n\), the coefficient is -3

To combine the terms \(2n\) and \(-3n\), simply add their coefficients together: \(2 + (-3) = -1\). The result is \(-1\), which is then multiplied by the variable \(n\) to create \(-1n\), or simply \(-n\).
Understanding coefficients is crucial as they directly impact the outcome of simplifying algebraic expressions.

Variables are symbols that represent numbers or quantities in algebraic expressions. Commonly used variables include \(x\), \(y\), and \(n\), but any letter can be a variable. In the expression \(2n - 3n\), the variable is \(n\).
Variables allow us to work with unknowns or quantities that can change. They make it possible to generalize mathematical ideas and solve problems that include unspecified numbers.

• Variables are often used when the exact values are either unknown or can vary.
• They form the backbone of algebraic expressions and equations.

In the process of simplifying expressions by combining like terms, we focus on the coefficients but maintain the variable part constant. This means, as with \(2n - 3n\), our task is to recombine these terms into a simpler expression but still within the realm of \(n\), giving us \(-n\).
A strong grasp of how variables function aids greatly in understanding and solving algebraic problems.